AD7FO’s 2012-2016 Extra Class Syllabus Preparing for the Extra class license exam Author: Jack Tiley AD7FO Revision: 2.00 (February 20, 2013) Required For this class: · · · · · · Rev 2.00 Copy of ARRL Tenth Edition of the Extra Class License Manual or recent copy of the ARRL Handbook (both are available from ARRL or ham radio retailers). Scientific Calculator that you can operate. Available from stores like Wal-Mart and office supply stores for $15 or less. o Add, Subtract, Multiply and Divide o Base Ten Logarithms o Simple trigonometric functions o Squares, Square root A printed copy of this syllabus. Pencil/pen and note pad to take notes and work out problems Access to a computer with internet access at home or at a library to take practice exams. A desire to study, Learn and ask questions. Page 1 AD7FO’s 2012-2016 Extra Class Syllabus Amateur Radio Extra Class License Class Syllabus Author: Jack Tiley AD7FO This material is based on the July 1, 2012Extra Class Question Pool with additional information added to explain the answers. Questions are shown with the correct answer only, which in the authors view makes it easier when you see the other choices in your exam to identify the correct answer. Question numbers have been included so you can go to the ARRL Extra Class License Manual questions in the back of the manual to see the other answer choices and for the referenced page(s) in the License Manual that will provide further explanation of the subject. It is not required, that you have your own copy of the ARRL (American Radio Relay League) Extra class license manual for the class which is available for purchase from ARRL publication sales on the ARRL web site and through amateur radio dealers. If you want more technical detail the author suggests you acquire a copy of a recent ARRL Handbook to help you understand the topics covered in this syllabus. Handbooks a few years old are fine and frequently available for reasonable prices at hamfests. Many of the illustrations used were copied from the ARRL Handbook CD-ROM and scanned from the license manual with permission from the copyright owner, ARRL, as well as other public sites on the web. This document has been written to assist instructors and students and may be distributed freely as long as no charge for the material is made, except for reproduction costs associated with delivering paper copies or electronic copies on CD-ROM’s and this note of copyright permission is not removed. While every effort was made to insure the accuracy of the material herein, this material was prepared by an ordinary human, and there is always the possibility that a few typographical or other errors may remain. If you find any errors your feedback would be appreciated by the author who can be contacted at [email protected] . Additional information and resources to help you study for the Extra Class License can be found on the ARRL web site at www.arrl.org/eclm . This site has articles and resources for reference materials on all aspects of the exam questions and links to math tutorials for those who have not used any algebra or trigonometry recently (the level of math required for the Extra Class License is not that difficult to master). About the author A retired Electrical Engineer with 44 years’ experience ten years in the measurements/metrology field and thirty four years in the electronics and communications field with Hewlett Packard Test Instrument Group, now Agilent Technologies. Author contact Information: [email protected] Hobbies • Amateur Radio, Test Equipment, Electronics in general • Attending every hamfests I can, including Hamvention in Dayton Ohio • Developing and presenting technical training for amateur radio. Teaching and mentoring § I Teach Technician, General and Extra License Classes (with training materials I have written) § I wrote and taught Emcomm I training and have written training for the new 4th edition emcomm training course. § I have written 20+ other training presentations for amateur radio. Contact the author if you are interested in using them for your local amateur radio meetings. § ARRL Eastern Washington Technical Coordinator and Spokane County Technical specialist. § Technical training for the Spokane County ARES/RACES Group and the Inland Empire VHF Club Inland Empire VHF Club www.vhfclub.org § Director 2009 thru 2012 § President 2012- current Other ARRL Appointments: § ARRL VE (Volunteer Examiner) § ARRL Registered Instructor § ARRL Certified EMCOMM instructor Rev 2.00 Page 2 AD7FO’s 2012-2016 Extra Class Syllabus Guide to using this syllabus. Each question from the license manual is shown in bold type----- E1A04 The first two characters are the license class sub element number ---E1A04 ---for Extra class subelement 1. The next letter identifies the group in the sub element ---E1A04 -- and the groups are in alphabetical order. The last two characters are the question number in the group -- E1A04-- in numerical order starting with 01. If the question number is followed by another number in brackets, like 1A12 [97.301, 97.305], the number in Brackets refers to a specific regulation in part 97 0f the FCC rules governing amateur radio. This Syllabus was written to teach the material not just teach the answers, although it can be used that way. When the Author teaches this class it includes equipment and theory demonstrations and “chalk Talk”. If you plan to teach classes using this syllabus visit the Inland Empire VHF Club website at www.vhfclub.org contact the author for a copy of the instructors guide. The author offers additional explanations and graphics when felt that it would aid in understanding. These explanations and comments and explanations are shown in bold blue italicized text as shown below: Telemetry is a technology that allows the remote measurement ……………………………. In problems involving math solutions are shown with precision that may be greater than the test answers (they may be rounded up or down) to allow you to verify your own solution to the problem. The following is an example: Z= SQR(X² + (XL –Xc)²) or Z= SQR( 400² + (0 - 300)²) or Z= SQR(250,000) or Z= 500 Ω Angle is arc tan (reactance/resistance) or arc tan (300/400) or arc tan (.75) or 36.86° The author suggests you look at the number of questions in each sub element and if there is one element you find particularly difficult consider concentrating on those areas you find easier to learn. Keep in mind you need a 74% passing score on the 50 question exam (you can get 13 wrong and still pass). If you can, find a local Ham to “Elmer” you on the difficult areas or locate a formal class in your area (check ARRL web site and local club web sites for listings). You can also check the ARRL Web Site or ARRL Section Web Sites for a volunteer Technical Specialist in your area who may be able provide some “Elmering” as well. While studying take the online exams that are available from a number of sites to check your progress and for review: http://aa9pw.com/radio/ http://www.eham.net/exams/ http://www.qrz.com/ham/ Check with the author at [email protected] the www.vhfclub.org web site if you are using this syllabus to make sure you have the latest revision. Rev 2.00 Page 3 AD7FO’s 2012-2016 Extra Class Syllabus SYLLABUS SUBELEMENT E1 - COMMISSION’S RULES [6 Exam Questions - 6 Groups] E1A Operating Standards: frequency privileges; emission standards; automatic message forwarding; frequency sharing; stations aboard ships or aircraft E1B Station restrictions and special operations: restrictions on station location; general operating restrictions, spurious emissions, control operator reimbursement; antenna structure restrictions; RACES operations E1C Station control: definitions and restrictions pertaining to local, automatic and remote control operation; control operator responsibilities for remote and automatically controlled stations E1D Amateur Satellite service: definitions and purpose; license requirements for space stations; available frequencies and bands; telecommand and telemetry operations; restrictions, and special provisions; notification requirements E1E Volunteer examiner program: definitions, qualifications, preparation and administration of exams; accreditation; question pools; documentation requirements E1F Miscellaneous rules: external RF power amplifiers; national quiet zone; business communications; compensated communications; spread spectrum; auxiliary stations; reciprocal operating privileges; IARP and CEPT licenses; third party communications with foreign countries; special temporary authority SUBELEMENT E2 - OPERATING PROCEDURES [5 Exam Questions - 5 Groups] E2A Amateur radio in space: amateur satellites; orbital mechanics; frequencies and modes; satellite hardware; satellite operations E2B Television practices: fast scan television standards and techniques; slow scan television standards and techniques E2C Operating methods: contest and DX operating; spread-spectrum transmissions; selecting an operating frequency E2D Operating methods: VHF and UHF digital modes; APRS E2E Operating methods: operating HF digital modes; error correction SUBELEMENT E3 - RADIO WAVE PROPAGATION [3 Exam Questions - 3 Groups] E3A Propagation and technique, Earth-Moon-Earth communications; meteor scatter E3B Propagation and technique, trans-equatorial; long path; gray-line; multi-path propagation E3C Propagation and technique, Aurora propagation; selective fading; radio-path horizon; take-off angle over flat or sloping terrain; effects of ground on propagation; less common propagation modes SUBELEMENT E4 - AMATEUR PRACTICES [5 Exam Questions - 5 Groups] E4A Test equipment: analog and digital instruments; spectrum and network analyzers, antenna analyzers; oscilloscopes; testing transistors; RF measurements E4B Measurement technique and limitations: instrument accuracy and performance limitations; probes; techniques to minimize errors; measurement of "Q"; instrument calibration E4C Receiver performance characteristics, phase noise, capture effect, noise floor, image rejection, MDS, signal-to-noise-ratio; selectivity Rev 2.00 Page 4 AD7FO’s 2012-2016 Extra Class Syllabus E4D Receiver performance characteristics, blocking dynamic range, intermodulation and cross-modulation interference; 3rd order intercept; desensitization; pre-selection E4E Noise suppression: system noise; electrical appliance noise; line noise; locating noise sources; DSP noise reduction; noise blankers SUBELEMENT E5 - ELECTRICAL PRINCIPLES [4 Exam Questions - 4 Groups] E5A Resonance and Q: characteristics of resonant circuits: series and parallel resonance; Q; half-power bandwidth; phase relationships in reactive circuits E5B Time constants and phase relationships: RLC time constants: definition; time constants in RL and RC circuits; phase angle between voltage and current; phase angles of series and parallel circuits E5C Impedance plots and coordinate systems: plotting impedances in polar coordinates; rectangular coordinates E5D AC and RF energy in real circuits: skin effect; electrostatic and electromagnetic fields; reactive power; power factor; coordinate systems SUBELEMENT E6 - CIRCUIT COMPONENTS [6 Exam Questions - 6 Groups] E6A Semiconductor materials and devices: semiconductor materials germanium, silicon, P-type, N-type; transistor types: NPN, PNP, junction, field-effect transistors: enhancement mode; depletion mode; MOS; CMOS; N-channel; P-channel E6B Semiconductor diodes E6C Integrated circuits: TTL digital integrated circuits; CMOS digital integrated circuits; gates E6D Optical devices and toroids: cathode-ray tube devices; charge-coupled devices (CCDs); liquid crystal displays (LCDs); toroids: permeability, core material, selecting, winding E6E Piezoelectric crystals and MMICs: quartz crystals; crystal oscillators and filters; monolithic amplifiers E6F Optical components and power systems: photoconductive principles and effects, photovoltaic systems, optical couplers, optical sensors, and optoisolators SUBELEMENT E7 - PRACTICAL CIRCUITS [8 Exam Questions - 8 Groups] E7A Digital circuits: digital circuit principles and logic circuits: classes of logic elements; positive and negative logic; frequency dividers; truth tables E7B Amplifiers: Class of operation; vacuum tube and solid-state circuits; distortion and intermodulation; spurious and parasitic suppression; microwave amplifiers E7C Filters and matching networks: filters and impedance matching networks: types of networks; types of filters; filter applications; filter characteristics; impedance matching; DSP filtering E7D Power supplies and voltage regulators E7E Modulation and demodulation: reactance, phase and balanced modulators; detectors; mixer stages; DSP modulation and demodulation; software defined radio systems E7F Frequency markers and counters: frequency divider circuits; frequency marker generators; frequency counters E7G Active filters and op-amps: active audio filters; characteristics; basic circuit design; operational amplifiers E7H Oscillators and signal sources: types of oscillators; synthesizers and phase-locked loops; direct digital synthesizers Rev 2.00 Page 5 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E8 - SIGNALS AND EMISSIONS [4 Exam Questions - 4 Groups] E8A AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; pulse and digital signal waveforms E8B Modulation and demodulation: modulation methods; modulation index and deviation ratio; pulse modulation; frequency and time division multiplexing E8C Digital signals: digital communications modes; CW; information rate vs. bandwidth; spread-spectrum communications; modulation methods E8D Waves, measurements, and RF grounding: peak-to-peak values, polarization; RF grounding SUBELEMENT E9 - ANTENNAS AND TRANSMISSION LINES [8 Exam Questions - 8 Groups] E9A Isotropic and gain antennas: definition; used as a standard for comparison; radiation pattern; basic antenna parameters: radiation resistance and reactance, gain, beam width, efficiency E9B Antenna patterns: E and H plane patterns; gain as a function of pattern; antenna design; Yagi antennas E9C Wire and phased vertical antennas: beverage antennas; terminated and resonant rhombic antennas; elevation above real ground; ground effects as related to polarization; take-off angles E9D Directional antennas: gain; satellite antennas; antenna beamwidth; losses; SWR bandwidth; antenna efficiency; shortened and mobile antennas; grounding E9E Matching: matching antennas to feed lines; power dividers E9F Transmission lines: characteristics of open and shorted feed lines: 1/8 wavelength; 1/4 wavelength; 1/2 wavelength; feed lines: coax versus open-wire; velocity factor; electrical length; transformation characteristics of line terminated in impedance not equal to characteristic impedance E9G The Smith chart E9H Effective radiated power; system gains and losses; radio direction finding antennas SUBELEMENT E0 – SAFETY - [1 exam question -– 1 group] E0A Safety: amateur radio safety practices; RF radiation hazards; hazardous materials Rev 2.00 Page 6 AD7FO’s 2012-2016 Extra Class Syllabus Rev 2.00 Page 7 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E1 - COMMISSION’S RULES [6 Exam Questions - 6 Groups] E1A Operating Standards: frequency privileges; emission standards; automatic message forwarding; frequency sharing; stations aboard ships or aircraft message forwarding; frequency sharing; FCC license actions; stations aboard ships or aircraft Carrier Frequency Lower Side band Carrier Frequency -2.8 KHz Carrier Frequency - 300 Hz Upper Side band Carrier Frequency +300 Hz Carrier Frequency +2.8 KHz E1A01 [97.301, 97.305] When using a transceiver that displays the carrier frequency of phone signals, which of the following displayed frequencies represents the highest frequency at which a properly adjusted USB emission will be totally within the band? 3 kHz below the upper band edge In an upper sideband transmission the modulation will be up to 3 KHz above the carrier frequency set on the transmitter frequency display, therefore the carrier frequency must be 3 KHz below the band edge to insure you do not transmit sidebands out of band. E1A02 [97.301, 97.305] When using a transceiver that displays the carrier frequency of phone signals, which of the following displayed frequencies represents the lowest frequency at which a properly adjusted LSB emission will be totally within the band? 3 kHz above the lower band edge In a lower sideband transmission the modulation side band will be 300 Hz to 3 KHz below the carrier frequency set on the transmitter frequency dial, therefore the carrier frequency must be 3 KHz above the band edge to insure you do not transmit out of band. E1A03 [97.301, 97.305] With your transceiver displaying the carrier frequency of phone signals, you hear a DX station's CQ on 14.349 MHz USB. Is it legal to return the call using upper sideband on the same frequency? No, my sidebands will extend beyond the band edge The 20 meter band is from 14.000 MHz to 14.350 MHz. When SSB modulation is applied to a carrier of 14.349 it would generate a sideband up to 14.352 which exceeds the 14.350 MHz upper frequency limit. E1A04 [97.301, 97.305] With your transceiver displaying the carrier frequency of phone signals, you hear a DX station calling CQ on 3.601 MHz LSB. Is it legal to return the call using lower sideband on the same frequency? No, my sidebands will extend beyond the edge of the phone band segment Adding the - 3 KHz for the modulation sideband would yield a lower frequency of 3.598 which places it in the RTTY and CW segment of the 80 meter band. (3.601 MHz - .003 MHz = 3.598 MHz) Rev 2.00 Page 8 AD7FO’s 2012-2016 Extra Class Syllabus E1A05 [97.313] What is the maximum power output permitted on the 60 meter band? 100 watts PEP effective radiated power relative to the gain of a half-wave dipole Effective radiated power is equal to the transmitter output power – the feed line loss + the antenna gain relative to a dipole (if you are not using a dipole). For example a station with 200 watts of output power and 3 dB transmission line loss using a dipole antenna would be legal. Remember that a 3 dB loss =0.5 times and a 3dB gain is 2 times. (With 200 watts of transmit power times the line loss which is 0.5 would leave 100 watts PEP with a dipole) E1A06 [97.303] Which of the following describes the rules for operation on the 60 meter band? Operation is restricted to specific emission types and specific channels E1A07 [97.303] What is the only amateur band where transmission on specific channels rather than a range of frequencies is permitted? 60 meter band E1A08 [97.219] If a station in a message forwarding system inadvertently forwards a message that is in violation of FCC rules, who is primarily accountable for the rules violation? The control operator of the originating station E1A09 [97.219] What is the first action you should take if your digital message forwarding station inadvertently forwards a communication that violates FCC rules? Discontinue forwarding the communication as soon as you become aware of it E1A10 [97.11] If an amateur station is installed aboard a ship or aircraft, what condition must be met before the station is operated? Its operation must be approved by the master of the ship or the pilot in command of the aircraft E1A11 [97.5] What authorization or licensing is required when operating an amateur station aboard a US-registered vessel in international waters? Rev 2.00 Page 9 AD7FO’s 2012-2016 Extra Class Syllabus Any FCC-issued amateur license or a reciprocal permit for an alien amateur licensee E1A12 [97.301, 97.305] With your transceiver displaying the carrier frequency of CW signals, you hear a DX station's CQ on 3.500 MHz. Is it legal to return the call using CW on the same frequency? No, sidebands from the CW signal will be out of the band. The CW portion of the 80 meter band extends from 3.50 to 3.60. A signal at 3.50 MHz would have sidebands that would be out of band E1A13 [97.5] Who must be in physical control of the station apparatus of an amateur station aboard any vessel or craft that is documented or registered in the United States? Any person holding an FCC-issued amateur license or who is authorized for alien reciprocal operation E1B Station restrictions and special operations: restrictions on station location; general operating restrictions; spurious emissions, control operator reimbursement; antenna structure restrictions; RACES operations E1B01 [97.3] Which of the following constitutes a spurious emission? An emission outside its necessary bandwidth that can be reduced or eliminated without affecting the information transmitted E1B02 [97.13] Which of the following factors might cause the physical location of an amateur station apparatus or antenna structure to be restricted? The location is of environmental importance or significant in American history, architecture, or culture E1B03 [97.13] Within what distance must an amateur station protect an FCC monitoring facility from harmful interference? 1 mile E1B04 [97.13, 1.1305-1.1319] What must be done before placing an amateur station within an officially designated wilderness area or wildlife preserve, or an area listed in the National Register of Historical Places? An Environmental Assessment must be submitted to the FCC E1B05 [97.303] What is the maximum bandwidth for a data emission on 60 meters? 2.8 kHz Rev 2.00 Page 10 AD7FO’s 2012-2016 Extra Class Syllabus E1B06 [97.15] Which of the following additional rules apply if you are installing an amateur station antenna at a site at or near a public use airport? You may have to notify the Federal Aviation Administration and register it with the FCC as required by Part 17 of FCC rules E1B07 [97.15] Where must the carrier frequency of a CW signal be set to comply with FCC rules for 60 meter operation? At the center frequency of the channel E1B08 [97.121] What limitations may the FCC place on an amateur station if its signal causes interference to domestic broadcast reception, assuming that the receiver(s) involved are of good engineering design? The amateur station must avoid transmitting during certain hours on frequencies that cause the interference “The amateur station shall not be operated during the hours of 8 p.m., local time to 10:30 p.m. local time and on Sunday for an additional period of 1:30 a.m. and 1 p.m., local time upon the frequency or frequencies used when interference is created”. E1B09 [97.407] Which amateur stations may be operated in RACES? Any FCC-licensed amateur station certified by the responsible civil defense organization for the area serve E1B10 [97.407] What frequencies are authorized to an amateur station participating in RACES? All amateur service frequencies authorized to the control operator E1B11 [97.307] What is the permitted mean power of any spurious emission relative to the mean power of the fundamental emission from a station transmitter or external RF amplifier installed after January 1, 2003, and transmitting on a frequency below 30 MHZ? At least 43 dB below E1B12 [97.307] What is the highest modulation index permitted at the highest modulation frequency for angle modulation? 1.0 Modulation index is equal to the peak deviation divided by the modulation rate (frequency). For example a signal with a peak deviation of 5 KHz and a 1 KHz modulation frequency would have a modulation index of 5 KHz/1 KHz or 5. Therefore a 2.8 KHz Maximum audio frequency could not have more than 2.8 KHz of peak deviation in order to meet the mode index of 1 requirement. E1C Station Control: Definitions and restrictions pertaining to local, automatic and remote control operation; control operator responsibilities for remote and automatically controlled stations Rev 2.00 Page 11 AD7FO’s 2012-2016 Extra Class Syllabus E1C01 [97.3] What is a remotely controlled station? A station controlled indirectly through a control link E1C02 [97.3, 97.109] What is meant by automatic control of a station? The use of devices and procedures for control so that the control operator does not have to be present at a control point E1C03 [97.3, 97.109] How do the control operator responsibilities of a station under automatic control differ from one under local control? Under automatic control the control operator is not required to be present at the control point E1C04 [97.109] When may an automatically controlled station retransmit third party communications? Only when transmitting RTTY or data emissions E1C05 [97.109] When may an automatically controlled station originate third party communications? Never EC106 Which of the following statements concerning remotely controlled amateur stations is true? A control operator must be present at the control point E1C07 [97.3] What is meant by local control? Direct manipulation of the transmitter by a control operator E1C08 [97.213] What is the maximum permissible duration of a remotely controlled station’s transmissions if its control link malfunctions? 3 minutes E1C09 [97.205] Which of these frequencies are available for an automatically controlled repeater operating below 30 MHz? 29.500 - 29.700 MHz E1C10 [97.113] What types of amateur stations may automatically retransmit the radio signals of other amateur stations? Only auxiliary, repeater or space stations E1D Amateur Satellite service: definitions and purpose; license requirements for space stations; available frequencies and bands; telecommand and telemetry operations; restrictions and special provisions; notification requirements E1D01 [97.3] What is the definition of the term telemetry? One-way transmission of measurements at a distance from the measuring instrument Rev 2.00 Page 12 AD7FO’s 2012-2016 Extra Class Syllabus E1D02 [97.3] What is the amateur satellite service? A radio communications service using amateur radio stations on satellites E1D03 [97.3] What is a telecommand station in the amateur satellite service? An amateur station that transmits communications to initiate, modify or terminate functions of a space station E1D04 [97.3] What is an Earth station in the amateur satellite service? An amateur station within 50 km of the Earth's surface intended for communications with amateur stations by means of objects in space E1D05 [97.207] What class of licensee is authorized to be the control operator of a space station? All classes Assuming the space station emissions are in a band authorized by that class of operator E1D06 [97.207] Which of the following special provisions must a space station incorporate in order to comply with space station requirements? The space station must be capable of terminating transmissions by telecommand when directed by the FCC E1D07 [97.207] Which amateur service HF bands have frequencies authorized to space stations? Only 40m, 20m, 17m, 15m, 12m and 10m Not on the 80m, 60m, 30m E1D08 [97.207] Which VHF amateur service bands have frequencies available for space stations? 2 meters Note: this question specifically asks for frequencies authorized in the VHF Band. There are no frequencies available on the 6 meter or 1.25 meter bands, some other choices shown are authorized but are not in the VHF band. E1D09 [97.207] THIS QUESTION HAS BEEN REMOVED FROM THE QUESTIPON POOL Which amateur service UHF bands have frequencies available for a space station? 70 cm, 23 cm, 13 cm E1D10 [97.211] Which amateur stations are eligible to be telecommand stations? Any amateur station so designated by the space station licensee, subject to the privileges of the class of operator license held by the control operator Rev 2.00 Page 13 AD7FO’s 2012-2016 Extra Class Syllabus E1D11 [97.209] Which amateur stations are eligible to operate as Earth stations? Any amateur station, subject to the privileges of the class of operator license held by the control operator E1E Volunteer examiner program: definitions; qualifications; preparation and administration of exams; accreditation; question pools; documentation requirements E1E01 [97.509] What is the minimum number of qualified VEs required to administer an Element 4 amateur operator license examination? Three E1E02 [97.523] Where are the questions for all written US amateur license examinations listed? In a question pool maintained by all the VECs E1E03 [97.521] What is a Volunteer Examiner Coordinator? An organization that has entered into an agreement with the FCC to coordinate amateur operator license examinations The two groups authorized are ARRL VEC and W5YI Group E1E04 [97.509, 97.525] Which of the following best describes the Volunteer Examiner accreditation process? The procedure by which a VEC confirms that the VE applicant meets FCC requirements to serve as an examiner E1E05 [97.503] What is the minimum passing score on amateur operator license examinations? Minimum passing score of 74% E1E06 [97.509] Who is responsible for the proper conduct and necessary supervision during an amateur operator license examination session? Each administering VE E1E07 [97.509] What should a VE do if a candidate fails to comply with the examiner’s instructions during an amateur operator license examination? Immediately terminate the candidate’s examination E1E08 [97.509] To which of the following examinees may a VE not administer an examination? Relatives of the VE as listed in the FCC rules YOU Siblings Rev 2.00 Spouse Other Relative s Page 14 AD7FO’s 2012-2016 Extra Class Syllabus E1E09 [97.509] What may be the penalty for a VE who fraudulently administers or certifies an examination? Revocation of the VE’s amateur station license grant and the suspension of the VE’s amateur operator license grant All those testing in a fraudulently administered exam must retest for their license. E1E10 [97.509] What must the administering VEs do after the administration of a successful examination for an amateur operator license? They must submit the application document to the coordinating VEC according to the coordinating VEC instructions E1E11 [97.509] What must the VE team do if an examinee scores a passing grade on all examination elements needed for an upgrade or new license? Three VEs must certify that the examinee is qualified for the license grant and that they have complied with the administering VE requirements E1E12 [97.509] What must the VE team do with the application form if the examinee does not pass the exam? Return the application document to the examinee E1E13 [97.519] What are the consequences of failing to appear for re-administration of an examination when so directed by the FCC? The licensee's license will be cancelled E1E14 [97.527] For which types of out-of-pocket expenses do the Part 97 rules state that VEs and VECs may be reimbursed? Preparing, processing, administering and coordinating an examination for an amateur radio license E1F Miscellaneous rules: external RF power amplifiers; national quiet zone; business communications; compensated communications; spread spectrum; auxiliary stations; reciprocal operating privileges; IARP and CEPT licenses; third party communications with foreign countries; special temporary authority E1F01 [97.305] On what frequencies are spread spectrum transmissions permitted? Only on amateur frequencies above 222 MHz E1F02 [97.5] Which of the following operating arrangements allows an FCC-licensed US citizen to operate in many European countries, and alien amateurs from many European countries to operate in the US? CEPT agreement E1F03 [97.315] Under what circumstances may a dealer sell an external RF power amplifier capable of operation below 144 MHz if it has not been granted FCC certification? It was purchased in used condition from an amateur operator and is sold to another amateur operator for use at that operator's station Rev 2.00 Page 15 AD7FO’s 2012-2016 Extra Class Syllabus E1F04 [97.3] Which of the following geographic descriptions approximately describes "Line A"? A line roughly parallel to and south of the US-Canadian border E1F05 [97.303] Amateur stations may not transmit in which of the following frequency segments if they are located in the contiguous 48 states and north of Line A? 420 - 430 MHz The 70 cm band covers from 420 MHz thru 450 MHz. Most voice communication takes place between 440 MHz and 450 MHz. E1F06 [97.3] What is the National Radio Quiet Zone? An area surrounding the National Radio Astronomy Observatory The National Radio Astronomy Observatory sites are located in Green Bank West Virginia, Socorro New Mexico, and Charlottesville NC. E1F07 [97.113] When may an amateur station send a message to a business? When neither the amateur nor his or her employer has a pecuniary interest in the communications E1F08 [97.113] Which of the following types of amateur station communications are prohibited? Communications transmitted for hire or material compensation, except as otherwise provided in the rules E1F09 [97.311] Which of the following conditions apply when transmitting spread spectrum emission? A. A station transmitting SS emission must not cause harmful interference to other stations employing other authorized emissions B. The transmitting station must be in an area regulated by the FCC or in a country that permits SS emissions C. The transmission must not be used to obscure the meaning of any communication D. All of these choices are correct E1F10 [97.313] What is the maximum transmitter power for an amateur station transmitting spread spectrum communications? 10 W E1F11 [97.317] Which of the following best describes one of the standards that must be met by an external RF power amplifier if it is to qualify for a grant of FCC certification? It must satisfy the FCC's spurious emission standards when operated at the lesser of 1500 watts, or its full output power E1F12 [97.201] Who may be the control operator of an auxiliary station? Only Technician, General, Advanced or Amateur Extra Class operators Rev 2.00 Page 16 AD7FO’s 2012-2016 Extra Class Syllabus E1F13 [97.117] What types of communications may be transmitted to amateur stations in foreign countries? Communications incidental to the purpose of the amateur service and remarks of a personal nature E1F14 [1.931] Under what circumstances might the FCC issue a "Special Temporary Authority" (STA) to an amateur station? To provide for experimental amateur communications Rev 2.00 Page 17 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E2 - OPERATING PROCEDURES [5 Exam Questions - 5 Groups] E2A Amateur radio in space: amateur satellites; orbital mechanics; frequencies and modes; satellite hardware; satellite operations E2A01 What is the direction of an ascending pass for an amateur satellite? From south to north E2A02 What is the direction of a descending pass for an amateur satellite? From north to south E2A03 What is the orbital period of an Earth satellite? The time it takes for a satellite to complete one revolution around the Earth E2A04 What is meant by the term mode as applied to an amateur radio satellite? The satellite's uplink and downlink frequency bands E2A05 What do the letters in a satellite's mode designator specify? The uplink and downlink frequency ranges The following table summarizes the mode designators: Mode Satellite Receiving Satellite Transmitting V/H VHF HF U/V UHF VHF V/U VHF UHF L/U L-Band UHF E2A06 On what band would a satellite receive signals if it were operating in mode U/V? 435-438 MHz E2A07 Which of the following types of signals can be relayed through a linear transponder? A. FM and CW B. SSB and SSTV C. PSK and Packet D. All of these choices are correct E2A08 Why should effective radiated power to a satellite which uses a linear transponder be limited? To avoid reducing the downlink power to all other users In a linear transponder the largest received signal sets the transponder output power. Signals less than the larger signal are attenuated and therefore are re-sent at a lower power than the larger signal. Using the minimum power needed to access the transponder will allow more users to have access to the transponder. Rev 2.00 Page 18 AD7FO’s 2012-2016 Extra Class Syllabus E2A09 What do the terms L band and S band specify with regard to satellite communications? The 23 centimeter and 13 centimeter bands Wave Guide Band Designator L Frequency Range ~ 1 GHz to 2 GHz S ~2 GHz to 4 GHz G 3.95 GHz to 5.85 GHz 4.9 GHz to 7.o5 GHz 7.05 GHz to 10 GHz C H X KU 8.2 GHZ to 12.4 GHz 12.4 GHz to 18 GHz K 18 GHz to 26.5 GHz KA 26.5 GHz to 40 GHz E2A10 Why may the received signal from an amateur satellite exhibit a rapidly repeating fading effect? Because the satellite is spinning Satellite designers often spin the satellite to improve its pointing stability so a rapid fading effect can be due to satellite rotation E2A11 What type of antenna can be used to minimize the effects of spin modulation and Faraday rotation? A circularly polarized antenna E2A12 What is one way to predict the location of a satellite at a given time? By calculations using the Keplerian elements for the specified satellite Example Keplerian Data from monthly ARRL report Satellite AO-07 1 07530U 74089B 12030.76241720 -.00000027 +00000-0 +10000-3 0 02940 2 07530 101.3983 033.3460 0011821 193.4266 166.6489 12.53587393702707 Satellite AO-16 1 20439U 90005D 12030.88295038 +.00000148 +00000-0 +70839-4 0 04002 2 20439 098.4139 338.2452 0010117 206.4703 153.5962 14.32012962150202 Satellite AO-27 1 22825U 93061C 12030.93151253 +.00000113 +00000-0 +61456-4 0 00344 2 22825 098.5601 336.0086 0008243 332.3578 027.7165 14.29425966956729 E2A13 What type of satellite appears to stay in one position in the sky? Geostationary Rev 2.00 Page 19 AD7FO’s 2012-2016 Extra Class Syllabus E2B Television practices: fast scan television standards and techniques; slow scan television standards and techniques E2B01 How many times per second is a new frame transmitted in a fast-scan (NTSC) television system? 30 E2B02 How many horizontal lines make up a fast-scan (NTSC) television frame? 525 E2B03 How is an interlaced scanning pattern generated in a fast-scan (NTSC) television system? By scanning odd numbered lines in one field and even numbered ones in the next It takes two frames to generate a complete picture. This interleaving makes the transition from one complete frame to another appear smoother. E2B04 What is blanking in a video signal? Turning off the scanning beam while it is traveling from right to left or from bottom to top See graphic from question E2B02 E2B05 Which of the following is an advantage of using vestigial sideband for standard fast- scan TV transmissions? Vestigial sideband reduces bandwidth while allowing for simple video detector circuitry Vestigial sideband (VSB) is a type of amplitude modulation (AM ) technique (sometimes called VSB-AM) that encodes data by varying the amplitude of a single carrier frequency . Portions of one of the redundant sidebands are removed to form a vestigial sideband signal - so-called because a vestige of the sideband remains. VSB transmission is similar to single-sideband (SSB) transmission, where one of the sidebands is completely removed. In a VSB transmission, however, the second sideband is not completely removed, but is filtered to remove all but the desired range of frequencies . This technology achieves much of the bandwidth reduction goal of SSB but the technology required to demodulate the signal is much simpler than that needed for pure SSB. E2B06 What is vestigial sideband modulation? Amplitude modulation in which one complete sideband and a portion of the other are transmitted E2B07 What is the name of the signal component that carries color information in NTSC video? Chroma A color TV signal starts off looking just like a black-and-white signal. An extra chrominance signal is added by superimposing a 3.579545 MHz sine wave onto the standard black-and-white signal following the horizontal sync pulse consisting of eight cycles of the 3.579545 MHz sine wave called the color burst Rev 2.00 Page 20 AD7FO’s 2012-2016 Extra Class Syllabus Following these eight cycles, a phase shift in the chrominance signal indicates the color to display. The amplitude of the signal determines the saturation. The following table shows you the relationship between color and phase: Color Phase Burst 0 degrees Yellow 15 degrees Red 75 degrees Magenta 135 degrees Blue 195 degrees Cyan 255 degrees Green 315 degrees E2B08 Which of the following is a common method of transmitting accompanying audio with amateur fast-scan television? A. Frequency-modulated sub-carrier B. A separate VHF or UHF audio link C. Frequency modulation of the video carrier D. All of these choices are correct E2B09 What hardware, other than a receiver with SSB capability and a suitable computer, is needed to decode SSTV using Digital Radio Mondiale (DRM)? No other hardware is needed DRM can deliver FM-comparable sound quality on frequencies below 30 MHz (long wave, medium wave and short wave), which allow for very-long-distance signal propagation. DRM is robust against the fading and interference which often plague conventional communication in these frequency ranges. The encoding and decoding can be performed with digital signal processing, so that a cheap embedded computer with a conventional transmitter and receiver can perform the rather complex encoding and decoding. E2B10 Which of the following is an acceptable bandwidth for Digital Radio Mondiale (DRM) based voice or SSTV digital transmissions made on the HF amateur bands? 3 KHz E2B11 What is the function of the Vertical Interval Signaling (VIS) code transmitted as part of an SSTV transmission? To identify the SSTV mode being used E2B12 How are analog SSTV images typically transmitted on the HF bands? Varying tone frequencies representing the video are transmitted using single sideband E2B13 How many lines are commonly used in each frame on an amateur slow-scan color television picture? 128 or 256 By comparison Fast scan TV uses 525 lines for each frame. See illustration for question E2B02 E2B14 What aspect of an amateur slow-scan television signal encodes the brightness of the picture? Tone frequency Rev 2.00 Page 21 AD7FO’s 2012-2016 Extra Class Syllabus E2B15 What signals SSTV receiving equipment to begin a new picture line? Specific tone frequencies E2B16 Which of the following is the video standard used by North American Fast Scan ATV stations? NTSC NTSC is an abbreviation for the National Television System Committee. This is the old analog television system that is used in most of North America, and still used for full motion amateur Television. Most countries using the NTSC standard are switching to newer digital television standards, of which at least four different ones are in use around the world. The first NTSC standard was developed in 1941 and had no provision for color television. In 1953 a second modified version of the NTSC standard was adopted, which allowed color television broadcasting compatible with the existing stock of black-and-white receivers. NTSC was the first widely adopted broadcast color system and remained dominant where it had been adopted until the first decade of the 21st century, when it was replaced with digital ATSC. E2B17 What is the approximate bandwidth of a slow-scan TV signal? 3 kHz E2B18 On which of the following frequencies is one likely to find FM ATV transmissions? 1,255 MHz E2B19 What special operating frequency restrictions are imposed on slow scan TV transmissions? They are restricted to phone band segments and their bandwidth can be no greater than that of a voice signal of the same modulation type E2C Operating methods: contest and DX operating; spread-spectrum transmissions; selecting an operating frequency E2C01 Which of the following is true about contest operating? Operators are permitted to make contacts even if they do not submit a log E2C02 Which of the following best describes the term “self-spotting” in regards to contest operating? The generally prohibited practice of posting one’s own call sign and frequency on a call sign spotting network DX operators use a web site to list DX stations they hear and work along with the band/frequency to help others make new and rare DX contacts. Is inappropriate list your own call and frequency on the DX spotting web site in order to gain more contacts by having operators come to you. E2C03 From which of the following bands is amateur radio contesting generally excluded? 30 meters The 30 meter band is only 50 KHz wide (10.100 MHz to 10.150 MHz and operators must avoid interference to fixed radio services outside the US. E2C04 On which of the following frequencies is an amateur radio contest contact generally discouraged? 146.52 MHz This is because 146.52 is the national calling frequency for 2 meters. Rev 2.00 Page 22 AD7FO’s 2012-2016 Extra Class Syllabus E2C05 What is the function of a DX QSL Manager? To handle the receiving and sending of confirmation cards for a DX station E2C06 During a VHF/UHF contest, in which band segment would you expect to find the highest level of activity? In the weak signal segment of the band, with most of the activity near the calling frequency CW and weak signal: National calling frequencies: 144.000 to 144.100 222.000 to 223.400 432.000 to 432.125 902.000 to 902.400 144.200 SSB and 146.52 FM 222.100 SSB and 223.500 FM 432.100 SSB and 446.000 FM 902.100 SSB E2C07 What is the Cabrillo format? A standard for submission of electronic contest logs E2C08 Why are received spread-spectrum signals resistant to interference? Signals not using the spectrum-spreading algorithm are suppressed in the receiver E2C09 How does the spread-spectrum technique of frequency hopping work? The frequency of the transmitted signal is changed very rapidly according to a particular sequence also used by the receiving station F4 F5 F2 F1 F6 F3 In a frequency hopping spread spectrum communication system the sender and receiver agree to change frequencies in a predetermined sequence. Sort of like the two frogs who are talking to each other as the hop in unison from one lily pad to another. If they hop together they can carry on a continuous conversation. In addition to knowing the frequency hopping sequence, the sender and receiver need to have a common starting time reference. E2C10 Why might a DX station state that they are listening on another frequency? A. Because the DX station may be transmitting on a frequency that is prohibited to some responding stations B. To separate the calling stations from the DX station C. To reduce interference, thereby improving operating efficiency D. All of these choices are correct E2C11 How should you generally identify your station when attempting to contact a DX station working a pileup or in a contest? Send your full call sign once or twice Rev 2.00 Page 23 AD7FO’s 2012-2016 Extra Class Syllabus E2C12 What might help to restore contact when DX signals become too weak to copy across an entire HF band a few hours after sunset? Switch to a lower frequency HF Band E2D Operating methods: VHF and UHF digital modes; APRS E2D01 Which of the following digital modes is especially designed for use for meteor scatter signals? FSK441 E2D02 What is the definition of baud? The number of data symbols transmitted per second. The baud rate can be higher than the bit rate if more than one parameter of the signal is changed during transmission, such as amplitude, width, or phase. If it takes ten bits to represent a single symbol then the bit rate will be 10 times the baud rate. E2D03 Which of the following digital modes is especially useful for EME communications? JT65 JT65 is also a low-power mode, even more so than PSK31. On the upper HF bands, you’ll often run 5W-10W or so. On the lower bands, 5W-10W will often do the trick, but for DX you might crank it up to 30W-40W if really needed. Some JT65-HF users are committed to 5W max, period. It is important not to crank up the power too much because it will make it hard or impossible for others to hear weaker signals, just like on PSK31. In most cases, 10W will be sufficient. This is an extremely efficient weak-signal mode E2D04 What is the purpose of digital store-and-forward functions on an Amateur Radio satellite? To store digital messages in the satellite for later download by other stations Sort of like a post office box you can send a message to and the recipient will go to that mailbox to retrieve your message. E2D05 Which of the following techniques is normally used by low Earth orbiting digital satellites to relay messages around the world? Store-and-forward E2D06 Which of the following is a commonly used 2-meter APRS frequency? 144.39 MHz E2D07 Which of the following digital protocols is used by APRS? AX.25 While there is no generally accepted formal definition of "protocol” but it is a set of agreed upon procedures to be followed when communicating digital data. E2D08 Which of the following types of packet frames is used to transmit APRS beacon data? Unnumbered Information E2D09 Under clear communications conditions, which of these digital communications modes has the fastest data throughput? 300-baud packet E2D10 How can an APRS station be used to help support a public service communications activity? Rev 2.00 Page 24 AD7FO’s 2012-2016 Extra Class Syllabus An APRS station with a GPS unit can automatically transmit information to show a mobile station's position during the event E2D11 Which of the following data are used by the APRS network communicate your location? Latitude and longitude E2D12 How does JT65 improve EME communications? It can decode signals many dB below the noise floor using FEC See explanation of JT65 for question E2D03 above E2E Operating methods: operating HF digital modes; error correction E2E01 Which type of modulation is common for data emissions below 30 MHz? FSK FSK is a digital method of transmission using Marks and spaces which are transmitted as one of two different frequencies of the transmitter carrier. FSK is true Frequency Shift Keying of the transmitter's carrier. This shift can be applied to any of the transmitter oscillators. Audio Frequency Shift Keying is generated by shifting the frequency of an audio oscillator that is fed into the transmitter's normal transmit audio input. Unlike FSK, AFSK can be used for FM modulation. E2E02 What do the letters FEC mean as they relate to digital operation? Forward Error Correction Forward error correction (FEC) is a method of obtaining error control in data transmission in which the source (transmitter) sends redundant data and the destination (receiver) recognizes only the portion of the data that contains no apparent errors. Because FEC does not require handshaking between the source and the destination, it can be used for broadcasting of data to many destinations simultaneously from a single source. Simple FEC is one of two modes used by radio amateurs in a self-correcting digital mode called AMTOR Mode B (an abbreviation for amateur teleprinting over radio). E2E03 How is Forward Error Correction implemented? By transmitting extra data that may be used to detect and correct transmission errors E2E04 What is indicated when one of the ellipses in an FSK crossed-ellipse display suddenly disappears? Selective fading has occurred In any radio transmission, the channel spectral response is not flat. It has dips or fades in the response due to reflections causing cancellation of certain frequencies at the receiver. Reflections off near-by objects (e.g. ground, buildings, trees, etc.) can lead to multipath signals of similar signal power as the direct signal. This can result in deep nulls in the received signal power due to destructive interference. For narrow bandwidth transmissions if the null in the frequency response occurs at the transmission frequency then the entire signal can be lost. E2E05 How does ARQ accomplish error correction? If errors are detected, a retransmission is requested E2E06 What is the most common data rate used for HF packet communications? 300 baud Rev 2.00 Page 25 AD7FO’s 2012-2016 Extra Class Syllabus E2E07 What is the typical bandwidth of a properly modulated MFSK16 signal? 316 Hz E2E08 Which of the following HF digital modes can be used to transfer binary files? PACTOR E2E09 Which of the following HF digital modes uses variable-length coding for bandwidth efficiency? PSK31 Like Morse Code where a character or letter can be represented by variable length bit streams from one to 5 bits of data. E is a single dit, I is two dits, S is 3 dits and H is 4 dits and the number 5 is represented by 5 dits. E2E10 Which of these digital communications modes has the narrowest bandwidth? PSK31 2E11 What is the difference between direct FSK and audio FSK? Direct FSK applies the data signal to the transmitter VFO E2E12 Which type of digital communication does not support keyboard-to-keyboard operation? Winlink Rev 2.00 Page 26 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E3 - RADIO WAVE PROPAGATION [3 Exam Questions - 3 Groups] E3A Propagation and technique: Earth-Moon-Earth communications (EME), meteor scatter E3A01 What is the approximate maximum separation measured along the surface of the Earth between two stations communicating by Moon bounce? 12,000 miles, as long as both can “see” the Moon E3A02 What characterizes libration fading of an Earth-Moon-Earth signal? A fluttery irregular fading E3A03 When scheduling EME contacts, which of these conditions will generally result in the least path loss? When the Moon is at perigee The moon is the closest to earth when it is at perigee most distant from earth it is at apogee. E3A04 What type of receiving system is desirable for EME communications? Equipment with very low noise figures Noise figure describes how much noise is added to the theoretical noise in dB for a given receiver band width. The theoretical noise of a perfect resistor at room temperature is approximately -174 dBm in a 1 Hertz bandwidth. The lower the noise figure of the receiver front end the better it can hear weak signals. A noise figure of around 0.25 dB for VHF and UHF is desired. E3A05 Which of the following describes a method of establishing EME contacts? Time synchronous transmissions with each station alternating When attempting an EME contact on 432 MHz two-and-one-half minute time sequences are used, where one station transmits for a full 2.5 minutes and then receives for the following 2.5 minutes. E3A06 What frequency range would you normally tune to find EME signals in the 2 meter band? 144.000 - 144.100 MHz E3A07 What frequency range would you normally tune to find EME signals in the 70 cm band? 432.000 - 432.100 MHz E3A08 When a meteor strikes the Earth's atmosphere, a cylindrical region of free electrons is formed at what layer of the ionosphere? The E layer E3A09 Which of the following frequency ranges is well suited for meteor-scatter communications? 28 - 148 MHz E3A10 Which of the following is a good technique for making meteor-scatter contacts? A. 15 second timed transmission sequences with stations alternating based on location B. Use of high speed CW or digital modes C. Short transmission with rapidly repeated call signs and signal reports Rev 2.00 Page 27 AD7FO’s 2012-2016 Extra Class Syllabus D. All of these choices are correct E3B Propagation and technique: trans-equatorial, long path, gray-line; multi-path propagation E3B01 What is transequatorial propagation? Propagation between two mid-latitude points at approximately the same distance north and south of the magnetic equator E3B02 What is the approximate maximum range for signals using transequatorial propagation? 5000 miles E3B03 What is the best time of day for transequatorial propagation? Afternoon or early evening E3B04 What type of propagation is probably occurring if an HF beam antenna must be pointed in a direction 180 degrees away from a station to receive the strongest signals? Long-path E3B05 Which amateur bands typically support long-path propagation? 160 to 10 meters E3B06 Which of the following amateur bands most frequently provides long-path propagation? 20 meters E3B07 Which of the following could account for hearing an echo on the received signal of a distant station? Receipt of a signal by more than one path E3B08 What type of HF propagation is probably occurring if radio signals travel along the terminator between daylight and darkness? Gray-line E3B09 At what time of day is gray-line propagation most likely to occur? At sunrise and sunset E3B10 What is the cause of gray-line propagation? At twilight, D-layer absorption drops while E-layer and F-layer propagation remain strong Rev 2.00 Page 28 AD7FO’s 2012-2016 Extra Class Syllabus E3B11 Which of the following describes gray-line propagation? Long distance communications at twilight on frequencies less than 15 MHz E3C Propagation and technique: Aurora propagation selective fading; radio-path horizon; take-off angle over flat or sloping terrain; effects of ground on propagation; less common propagation modes E3C01 Which of the following effects does Aurora activity have on radio communications? A. SSB signals are raspy B. Signals propagating through the Aurora are fluttery C. CW signals appear to be modulated by white noise D. All of these choices are correct E3C02 What is the cause of Aurora activity? The interaction of charged particles from the Sun with the Earth’s magnetic field and the ionosphere A solar flare propels charged particles into space through the solar wind. As the solar wind interacts with the earth’s magnetic field it can produce the northern lights and provide and charge the ionosphere which allow long distance propagation for our HF signals. We haven’t seen the northern lights much or had good propagation in recent years because the sun has been inactive. We plunged into a solar minimum in 2007 and have slowly begun to rebound out of it. The solar cycle from maximum to minimum and back takes 11 years. E3C03 Where in the ionosphere does Aurora activity occur? In the E-region E3C04 Which emission mode is best for Aurora propagation? CW E3C05 Which of the following describes selective fading? Partial cancellation of some frequencies within the received pass band E3C06 By how much does the VHF/UHF radio-path horizon distance exceed the geometric horizon? By approximately +15% of the distance Rev 2.00 Page 29 AD7FO’s 2012-2016 Extra Class Syllabus E3C07 How does the radiation pattern of a horizontally polarized 3-element beam antenna vary with its height above ground? The main lobe takeoff angle decreases with increasing height E3C08 What is the name of the high-angle wave in HF propagation that travels for some distance within the F2 region? Pedersen ray Paths 4 and 5 shown above are Pedersen rays or high-angle rays. These rays are not refracted sufficiently to return directly to the earth but don't have a high enough angle to penetrate (like ray 6). They get trapped in the ionosphere often exiting where there is a big gradient in electron density (at dusk and dawn). The plots below are the result of both high and low angle rays being present at the same time. An effect that we are normally unaware of! Given this model, we might reasonably expect to see four components on an oblique path as it fades out: o and x wave from the low angle path and o and x waves from the high angle path. Each with different Doppler shifts. E3C09 Which of the following is usually responsible for causing VHF signals to propagate for hundreds of miles? Tropospheric ducting The troposphere consists of atmospheric regions close to the Earth's surface. Slight bending of radio waves occur in the troposphere, causing signals to return to Earth beyond the geometric horizon, and allows you to contact stations that are farther away than would otherwise be possible. This radio path horizon is generally about 15% farther away than the visible horizon. During the spring, summer, and fall months, it is possible to make VHF and UHF contacts over long distances up to 1,000 miles or more. This occurs during certain weather conditions that cause tropospheric enhancement and tropospheric ducting. It is most useful in the VHF/UHF region. When such "tropo" openings occur, the VHF and UHF bands are filled with excited operators eager to work DX. The troposphere is the layer of the atmosphere just below the stratosphere. It extends upward approximately 7 to 10 miles. In this region clouds form and temperature decreases rapidly with altitude. E3C10 How does the performance of a horizontally polarized antenna mounted on the side of a hill compare with the same antenna mounted on flat ground? The main lobe takeoff angle decreases in the downhill direction Rev 2.00 Page 30 AD7FO’s 2012-2016 Extra Class Syllabus E3C11 From the contiguous 48 states, in which approximate direction should an antenna be pointed to take maximum advantage of aurora propagation? North E3C12 How does the maximum distance of ground-wave propagation change when the signal frequency is increased? It decreases E3C13 What type of polarization is best for ground-wave propagation? Vertical E3C14 Why does the radio-path horizon distance exceed the geometric horizon? Downward bending due to density variations in the atmosphere See illustration for E3C09 Rev 2.00 Page 31 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E4 - AMATEUR PRACTICES [5 Exam Questions - 5 Groups] E4A Test equipment: analog and digital instruments; spectrum and network analyzers, antenna analyzers; oscilloscopes; testing transistors; RF measurements Oscilloscope Spectrum Analyzer E4A01 How does a spectrum analyzer differ from an oscilloscope? A spectrum analyzer displays signals in the frequency domain; an oscilloscope displays signals in the time domain E4A02 Which of the following parameters would a spectrum analyzer display on the horizontal axis? Frequency E4A03 Which of the following parameters would a spectrum analyzer display on the vertical axis? Amplitude E4A04 Which of the following test instruments is used to display spurious signals from a radio transmitter? A spectrum analyzer Rev 2.00 Page 32 AD7FO’s 2012-2016 Extra Class Syllabus E4A05 Which of the following test instruments is used to display intermodulation distortion products in an SSB transmission? A spectrum analyzer If two separate (non-harmonically related) audio tones are applied to the the microphone input of a SSB transmitter we would expect to see only two signals in the RF output (Carrier ± tone 1 and the carrier ±tone2). In the illustration below you can see that there two smaller signals about 55dB bellow the two RF signals. These are intermodulation distortion products. E4A06 Which of the following could be determined with a spectrum analyzer? A. The degree of isolation between the input and output ports of a 2 meter duplexer B. Whether a crystal is operating on its fundamental or overtone frequency C. The spectral output of a transmitter D. All of these choices are correct E4A07 Which of the following is an advantage of using an antenna analyzer compared to an SWR bridge to measure antenna SWR? Antenna analyzers do not need an external RF source These are some common antenna analyzers. The one the far left is made by MFJ and is the most commonly used by amateur radio operator. E4A08 Which of the following instruments would be best for measuring the SWR of a beam antenna? An antenna analyzer E4A09 Which of the following describes a good method for measuring the intermodulation distortion of your own PSK signal? Transmit into a dummy load, receive the signal on a second receiver, and feed the audio into the sound card of a computer running an appropriate PSK program This is actually observing your own PSK Transmission. You should see only a single line on the waterfall display. Multiple signals mean you are driving the transmitter too hard and generating spurious intermodulation signal that would interfere with others. E4A10 Which of the following tests establishes that a silicon NPN junction transistor is biased on? Measure base-to-emitter voltage with a voltmeter; it should be approximately 0.6 to 0.7 volts Rev 2.00 Page 33 AD7FO’s 2012-2016 Extra Class Syllabus E4A11 Which of these instruments could be used for detailed analysis of digital signals? Oscilloscope E4A12 Which of the following procedures is an important precaution to follow when connecting a spectrum analyzer to a transmitter output? Attenuate the transmitter output going to the spectrum analyzer Transmitter Power Attenuator Spectrum Analyzer The attenuator acts as a dummy load for the transmitter and must handle the fill transmit output power while reducing the signal at its output to around 10 mW. For a 100 watt transmitter this would require 40dB of attenuation. E4B Measurement techniques: Instrument accuracy and performance limitations; probes; techniques to minimize errors; measurement of Q; instrument calibration E4B01 Which of the following factors most affects the accuracy of a frequency counter? Time base accuracy E4B02 What is an advantage of using a bridge circuit to measure impedance? The measurement is based on obtaining a signal null, which can be done very precisely E4B03 If a frequency counter with a specified accuracy of +/- 1.0 ppm reads 146,520,000 Hz, what is the most the actual frequency being measured could differ from the reading. 146.52 Hz Rev 2.00 Page 34 AD7FO’s 2012-2016 Extra Class Syllabus Parts per million can be expressed as hertz per MHz, for 146.52 Mhzsignal the error with a 1 ppm accuracy would be 146.52 times 1 Hz or ± 146.52 Hz E4B04 If a frequency counter with a specified accuracy of +/- 0.1 ppm reads 146,520,000 Hz, what is the most the actual frequency being measured could differ from the reading? 14.652 Hz Parts per million can be expressed as hertz per MHz, for 14.652 Mhzsignal the error with a 0.1 ppm accuracy would be 14.562 times .01 Hz or ± 14.652 Hz E4B05 If a frequency counter with a specified accuracy of +/- 10 ppm reads 146,520,000 Hz, what is the most the actual frequency being measured could differ from the reading? 1465.20 Hz Parts per million can be expressed as hertz per MHz, for 146.52 Mhzsignal the error with a 0.1 ppm accuracy would be 146.52 times 10 Hz or ± 1465.2 Hz E4B06 How much power is being absorbed by the load when a directional power meter connected between a transmitter and a terminating load reads 100 watts forward power and 25 watts reflected power? 75 watts The forward power is the power being accepted or absorbed by the load the 25 watts of reflected power is reflected back to the transmitter output circuit E4B07 Which of the following is good practice when using an oscilloscope probe? Keep the signal ground connection of the probe as short as possible Long ground leads may look like an inductor and therefore a high impedance to ground at rf and VHF frequencies. E4B08 Which of the following is a characteristic of a good DC voltmeter? High impedance input The higher the input impedance of the voltmeter the less it will load the circuit and influence the measurement. E4B09 What is indicated if the current reading on an RF ammeter placed in series with the antenna feed line of a transmitter increases as the transmitter is tuned to resonance? There is more power going into the antenna This is what you want to happen E4B10 Which of the following describes a method to measure intermodulation distortion in an SSB transmitter? Modulate the transmitter with two non-harmonically related audio frequencies and observe the RF output with a spectrum analyzer E4B11 How should a portable antenna analyzer be connected when measuring antenna resonance and feed point impedance? Connect the antenna feed line directly to the analyzer's connector Never connect an antenna analyzer to a transmitter or measure an antenna in close proximity to an active transmitting antenna. This could destroy the antenna analyzer. E4B12 What is the significance of voltmeter sensitivity expressed in ohms per volt? Rev 2.00 Page 35 AD7FO’s 2012-2016 Extra Class Syllabus The full scale reading of the voltmeter multiplied by its ohms per volt rating will provide the input impedance of the voltmeter E4B13 How is the compensation of an oscilloscope probe typically adjusted? A square wave is displayed and the probe is adjusted until the horizontal portions of the displayed wave are as nearly flat as possible E4B14 What happens if a dip meter is too tightly coupled to a tuned circuit being checked? A less accurate reading results E4B15 Which of the following can be used as a relative measurement of the Q for a series-tuned circuit? The bandwidth of the circuit's frequency response Rev 2.00 Page 36 AD7FO’s 2012-2016 Extra Class Syllabus E4C Receiver performance characteristics: phase noise; capture effect; noise floor; image rejection; MDS; signal-to-noise-ratio; selectivity E4C01 What is an effect of excessive phase noise in the local oscillator section of a receiver? It can cause strong signals on nearby frequencies to interfere with reception of weak signals E4C02 Which of the following portions of a receiver can be effective in eliminating image signal interference? A front-end filter or pre-selector Pre-selectors can be external and tunable or fixed as shown above. High performance receivers will have pre-selectors designed into the radio. E4C03 What is the term for the blocking of one FM phone signal by another, stronger FM phone signal? Capture effect FM receivers exhibit what I called the capture effect when a strong FM signal overpowers and eliminates a weaker FM signal on the same frequency. E4C04 What is the definition of the noise figure of a receiver? The ratio in dB of the noise generated by the receiver compared to the theoretical minimum noise The noise figure is a way of describing the amount of noise generated in a receiver, amp, transmission line, antenna system, or other component. The noise figure of a component or system is defined as the signal-to-noise ratio at the input divided by the signal-to-noise ratio at the output, with the input noise equal to the noise available from a matched resistance at a temperature of T0=290 Kelvin. E4C05 What does a value of -174 dBm/Hz represent with regard to the noise floor of a receiver? The theoretical noise at the input of a perfect receiver at room temperature (290° Kelvin) This noise floor will be higher as the receiver bandwidth is increased. A receiver with a 10 KHz bandwidth will have 10,000 times more noise or an additional 40dB of noise bringing the noise floor up to – 174dBm + 40 dB or -134 dBm. E4C06 A CW receiver with the AGC off has an equivalent input noise power density of -174 dBm/Hz. What would be the level of an un-modulated carrier input to this receiver that would yield an audio output SNR of 0 dB in a 400 Hz noise bandwidth? -148 dBm This noise floor will be higher as the receiver bandwidth is increased. A receiver with a 400 KHz bandwidth will have 4 00 times more noise or an additional 26 dB of noise bringing the noise floor up to – 174dBm + 26 dB or -148 dBm. dB= 10(log bw2/bw1) or dB= 10(log 400/1) dB= 10 (2.602) or dB=26 Rev 2.00 Page 37 AD7FO’s 2012-2016 Extra Class Syllabus Therefore the new noise floor will be -174 +26 or -148dBm E4C07 What does the MDS of a receiver represent? The minimum discernible signal E4C08 How might lowering the noise figure affect receiver performance? It would improve weak signal sensitivity E4C09 Which of the following choices is a good reason for selecting a high frequency for the design of the IF in a conventional HF or VHF communications receiver? Easier for front-end circuitry to eliminate image responses E4C10 Which of the following is a desirable amount of selectivity for an amateur RTTY HF receiver? 300 Hz E4C11 Which of the following is a desirable amount of selectivity for an amateur SSB phone receiver? 2.4 kHz E4C12 What is an undesirable effect of using too wide a filter bandwidth in the IF section of a receiver? Undesired signals may be heard E4C13 How does a narrow-band roofing filter affect receiver performance? It improves dynamic range by attenuating strong signals near the receive frequency Roofing filters are band-pass filters installed before or in the early stage of a receivers IF amplifier E4C14 On which of the following frequencies might a signal be transmitting which is generating a spurious image signal in a receiver tuned to 14.300 MHz and which uses a 455 kHz IF frequency? 15.210 MHz When a local oscillator signal is mixed with an incoming signal it generates the sum and the difference of the two signals. If we assume High side mix (the LO is higher than the tuned frequency then the LO will be the tuned frequency + 455KHz. A signal 455 KHz above the LO would also generate a 455 KHz IF spurious or image signal. So taking the receive frequency of 14.300 MHz and 2 times the IF frequency of 0.455 MHz (14.300 – (2x.455) we get 15.210 MHz. E4C15 What is the primary source of noise that can be heard from an HF receiver with an antenna connected? Atmospheric noise E4D Receiver performance characteristics: blocking dynamic range; intermodulation and crossmodulation interference; 3rd order intercept; desensitization; preselection E4D01 What is meant by the blocking dynamic range of a receiver? The difference in dB between the noise floor and the level of an incoming signal which will cause 1 dB of gain compression E4D02 Which of the following describes two problems caused by poor dynamic range in a communications receiver? Cross-modulation of the desired signal and desensitization from strong adjacent signals Rev 2.00 Page 38 AD7FO’s 2012-2016 Extra Class Syllabus E4D03 How can intermodulation interference between two repeaters occur? When the repeaters are in close proximity and the signals mix in the final amplifier of one or both transmitters E4D04 Which of the following may reduce or eliminate intermodulation interference in a repeater caused by another transmitter operating in close proximity? A properly terminated circulator at the output of the transmitter E4D05 What transmitter frequencies would cause an intermodulation-product signal in a receiver tuned to 146.70 MHz when a nearby station transmits on 146.52 MHz? 146.34 MHz and 146.61 MHz E4D06 What is the term for unwanted signals generated by the mixing of two or more signals? Intermodulation interference E4D07 Which of the following describes the most significant effect of an off-frequency signal when it is causing cross-modulation interference to a desired signal? The off-frequency unwanted signal is heard in addition to the desired signal E4D08 What causes intermodulation in an electronic circuit? Nonlinear circuits or devices E4D09 What is the purpose of the preselector in a communications receiver? To increase rejection of unwanted signals E4D10 What does a third-order intercept level of 40 dBm mean with respect to receiver performance? A pair of 40 dBm signals will theoretically generate a third-order intermodulation product with the same level as the input signals E4D11 Why are third-order intermodulation products created within a receiver of particular interest compared to other products? The third-order product of two signals which are in the band of interest is also likely to be within the band E4D12 What is the term for the reduction in receiver sensitivity caused by a strong signal near the received frequency? Desensitization E4D13 Which of the following can cause receiver desensitization? Strong adjacent-channel signals Rev 2.00 Page 39 AD7FO’s 2012-2016 Extra Class Syllabus E4D14 Which of the following is a way to reduce the likelihood of receiver desensitization? Decrease the RF bandwidth of the receiver E4E Noise suppression: system noise; electrical appliance noise; line noise; locating noise sources; DSP noise reduction; noise blankers E4E01 Which of the following types of receiver noise can often be reduced by use of a receiver noise blanker? Ignition noise E4E02 Which of the following types of receiver noise can often be reduced with a DSP noise filter? A. Broadband white noise B. Ignition noise C. Power line noise D. All of these choices are correct E4E03 Which of the following signals might a receiver noise blanker be able to remove from desired signals? Signals which appear across a wide bandwidth E4E04 How can conducted and radiated noise caused by an automobile alternator be suppressed? By connecting the radio's power leads directly to the battery and by installing coaxial capacitors in line with the alternator leads E4E05 How can noise from an electric motor be suppressed? By installing a brute-force AC-line filter in series with the motor leads E4E06 What is a major cause of atmospheric static? Thunderstorms E4E07 How can you determine if line noise interference is being generated within your home? By turning off the AC power line main circuit breaker and listening on a battery operated radio E4E08 What type of signal is picked up by electrical wiring near a radio antenna? A common-mode signal at the frequency of the radio transmitter Rev 2.00 Page 40 AD7FO’s 2012-2016 Extra Class Syllabus The principal aim of any data-transmission system is to send data from one location to another, whether within a single box or enclosure, between boxes within an enclosure, between enclosures within a building or defined area, or between buildings. Figure 1 illustrates an RS-485 signaling situation in which the buildings are supplied from different power circuits. E4E09 What undesirable effect can occur when using an IF noise blanker? Nearby signals may appear to be excessively wide even if they meet emission standards This is because a peak portion of the signal is removed and the broader lower section is only received. The observed 3 dB bandwidth of the blanked signal would appear to be much wider than if referred to the original peak signal level. E4E10 What is a common characteristic of interference caused by a touch controlled electrical device? A. The interfering signal sounds like AC hum on an AM receiver or a carrier modulated by 60 Hz hum on a SSB or CW receiver B. The interfering signal may drift slowly across the HF spectrum C. The interfering signal can be several kHz in width and usually repeats at regular intervals across a HF band D. All of these choices are correct E4E11 Which of the following is the most likely cause if you are hearing combinations of local AM broadcast signals within one or more of the MF or HF ham bands? Nearby corroded metal joints are mixing and re-radiating the broadcast signals Corroded joints act like diodes and then function as a mixer generating sum and difference frequencies from nearby strong signals. E4E12 What is one disadvantage of using some types of automatic DSP notch-filters when attempting to copy CW signals? The DSP filter can remove the desired signal at the same time as it removes interfering signals E4E13 What might be the cause of a loud roaring or buzzing AC line interference that comes and goes at intervals? A. Arcing contacts in a thermostatically controlled device B. A defective doorbell or doorbell transformer inside a nearby residence C. A malfunctioning illuminated advertising display D. All of these choices are correct E4E14 What is one type of electrical interference that might be caused by the operation of a nearby personal computer? The appearance of unstable modulated or unmodulated signals at specific frequencies Rev 2.00 Page 41 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E5 - ELECTRICAL PRINCIPLES [4 Exam Questions - 4 Groups] E5A Resonance and Q: characteristics of resonant circuits; series and parallel resonance; Q; halfpower bandwidth; phase relationships in reactive circuits E5A01 What can cause the voltage across reactances in series to be larger than the voltage applied to them? Resonance Resonance is when the inductive reactance and capacitive reactance are equal. In this condition the current flowing in the circuit is limited only by the circuit resistance. E5A02 What is resonance in an electrical circuit? The frequency at which the capacitive reactance equals the inductive reactance E5A03 What is the magnitude of the impedance of a series RLC circuit at resonance? Approximately equal to circuit resistance E5A04 What is the magnitude of the impedance of a circuit with a resistor, an inductor and a capacitor all in parallel, at resonance? Approximately equal to circuit resistance E5A05 What is the magnitude of the current at the input of a series RLC circuit as the frequency goes through resonance? Maximum E5A06 What is the magnitude of the circulating current within the components of a parallel LC circuit at resonance? It is at a maximum E5A07 What is the magnitude of the current at the input of a parallel RLC circuit at resonance? Minimum E5A08 What is the phase relationship between the current through and the voltage across a series resonant circuit at resonance? The voltage and current are in phase E5A09 What is the phase relationship between the current through and the voltage across a parallel resonant circuit at resonance? The voltage and current are in phase E5A10 What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 1.8 MHz and a Q of 95? 18.9 kHz BW= Frequency / Q or 1,800 KHz/95 or 18.94 KHz E5A11 What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 7.1 MHz and a Q of 150? 47.3 kHz BW= Frequency / Q or 7,100 KHz/150 or 47.3 KHz E5A12 What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118? 31.4 kHz BW= Frequency / Q or 3,700 KHz/118 or 31.36 KHz Rev 2.00 Page 42 AD7FO’s 2012-2016 Extra Class Syllabus E5A13 What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 14.25 MHz and a Q of 187? 76.2 kHz BW= Frequency / Q or 14,250 KHz/187 or 76.20 KHz E5A14 What is the resonant frequency of a series RLC circuit if R is 22 ohms, L is 50 micro-henrys and C is 40 picofarads? 3.56 MHz For frequency in MHz, Inductance in micro-henries and capacitance in picofarads: F(resonance) =1,000 / (2π√(L x C)) F(resonance)=1,000 / (2π√(L x C)) = 1,000 / (6.28√(50 x 40)) = 3.56 MHz E5A15 What is the resonant frequency of a series RLC circuit if R is 56 ohms, L is 40 micro-henrys and C is 200 picofarads? 1.78 MHz F(resonance)=1,000 / (2π√(L x C)) = 1,000 / (6.28√(40 x 200 )) = 1.78 MHz E5A16 What is the resonant frequency of a parallel RLC circuit if R is 33 ohms, L is 50 micro-henrys and C is 10 pico-farads? 7.12 MHz F(resonance)=1,000 / (2π√(L x C)) = 1,000 / (6.28√(50 x 10)) = 7.121 MHz E5A17 What is the resonant frequency of a parallel RLC circuit if R is 47 ohms, L is 25 micro-henrys and C is 10 picofarads? 10.1 MHz F(resonance)=1,000 / (2π√(L x C)) = 1,000 / (6.28√(25 x 10)) = 10.07 MHz E5B Time constants and phase relationships: RLC time constants; definition; time constants in RL and RC circuits; phase angle between voltage and current; phase angles of series and parallel circuits Time Constants Tutorial When a voltage is applied to a capacitor through a resistance (all circuits have resistance) it takes time for the voltage across the capacitor to reach the applied voltage. At the instant the voltage is applied the current in the circuit is at a maximum limited only by the circuit resistance. As time passes the voltage across the capacitor rises and the current decreases until the capacitor charge reaches the applied voltage at which point the current goes to zero. The voltage across the capacitor will rise to 63.2 % of the applied voltage in one time constant. The time constant in seconds is calculated by multiplying the resistance in megohms by the capacitance in microfarads. TC= R(ohms) x C(farads) Rev 2.00 or in terms of more common values --TC= R (megohms) x C(microfarads) Page 43 AD7FO’s 2012-2016 Extra Class Syllabus For example, 100 volts applied to 1µF capacitor with a series one megohm resistor will charge to 63.2 volts in one second. Remember that TC= R (megohms) x C(microfarads) or TC= 1x1 or 1 second and the charge after 1 time constant will be 63.2% of the applied 100 volts, or 63.2 volts E5B01 What is the term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the applied voltage? One time constant Time Constants Charge % of applied voltage Discharge % of starting voltage 63.2% 86.5% 95.0% 98.2% 99.3% 1 2 3 4 5 36.8% 13.5 % 5% 1.8% .7% E5B02 What is the term for the time it takes for a charged capacitor in an RC circuit to discharge to 36.8% of its initial voltage? One time constant One time constant discharge would be 100% - 63.2% or 36.8% E5B03 The capacitor in an RC circuit is discharged to what percentage of the starting voltage after two time constants? 13.5% %= (100-((100 x .632)) – (100 – (100 x.632) x .632)) or 100+(- 63.2 – 23.25) or 13.54% E5B04 What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors, all in parallel? 220 seconds TC (seconds) = R (megohms) x C (microfarads) TC =(1/2) x (220 x 2) TC= 0.5 x 440 TC= 220 seconds Remember that capacitors in parallel add and resistors of equal value in parallel are equal to one resistor divided by the number of resistors. E5B05 How long does it take for an initial charge of 20 V DC to decrease to 7.36 V DC in a 0.01-microfarad capacitor when a 2megohm resistor is connected across it? 0.02 seconds To discharge to 7.36 VDC would take one time constant with an initial charge of 20V – (.632 x 20V) or 7.36 Volts TC = 2 x .01 TC= 0 .02 seconds TC= 20 milliseconds E5B06 How long does it take for an initial charge of 800 V DC to decrease to 294 V DC in a 450-microfarad capacitor when a 1megohm resistor is connected across it? 450 seconds To discharge to 294 VDC would take one time constant 800V – (.632 x 800V) = 294.4V TC = 1 x 450 or 450 seconds Rev 2.00 Page 44 AD7FO’s 2012-2016 Extra Class Syllabus Trigonometry Tutorial For a number of problems associated with electronics involving series circuits of resistance and reactance and the Extra class Exam you will need a basic understanding of trigonometry. The problems center on a right triangle (that is a triangle that has one angle that is 90° and the sum of the remaining two angles is equal to 90°). Using trigonometric functions if we know two sides, or an angle (other than the 90°angle) and one side of the triangle we can calculate the remaining angles and dimensions. Examples: If X=3 and Y=4 then R=5 and θ = 53.1° If X=50 and Y=100 then R=111.80and θ = 63.4° If X=5 and Y=10 then R=11.18 and θ = 63.4° If X=153 and Y=52 then R=161.6 and θ = 18.77° The sides of the triangle are given names from the rectangular coordinate system with the horizontal side called X (also called the Adjacent side) and the vertical side is called Y (also called the opposite side) and the side connecting the X and Y sides is called the Hypotenuse called R in this example If two of the three sides are known the third side can be found using the following equation: Hypotenuse² = X² + Y² or as commonly expressed R = √(X²+Y²) There are 6 trigonometric functions that can be used to calculate the angle between X and R and between Y and R. We will focus on three of these functions; Sine, Cosine and Tangent to solve for the angle between the X side and the R side ( θ ). Sine of θ = Y / R Cosine of θ = X / R Tangent of θ = Y / X Secant = R/Y Cosecant = R/X Cotangent = X/Y Example 1: To find the angle, θ for a triangle with side X value of 3 and a side Y value of 6: Tangent of θ = 6 / 3 or 2.00. To find the angle enter 2 into your calculator and press the Arc Tan key which will show you the angle represented by the tangent value, in this case 2.00. The Arc Tan of 2 is 63.43°. Example 2: To find the angle, θ for a triangle with a side X value of 3 and a side Y value of 4: Tangent of θ = 4 / 3 or 1.333 To find the angle enter 1.333 into your calculator and press the Arc Tan(or Tan^-1 on some calculators) key which will show you 53.03° Example 3: To find the angle, θ for a triangle with a side X value of 12 and a side Y value of 12 Tangent of θ = 12/12 or 1 To find the angle enter 1 into your calculator and press the Arc Tan key which will show you 45.0° Reactance (AC resistance of capacitors and inductors) Capacitors and inductors exhibit a resistance to current flow much like a resistor but with values that change with the frequency of the applied circuit. The AC resistance of a capacitor is called capacitive reactance (Xc) and is calculated using the formula: Xc= 1/(2π x F x C) with C in µF and F in MHz Rev 2.00 Page 45 AD7FO’s 2012-2016 Extra Class Syllabus Examples: Find the capacitive reactance of a 1 µf capacitor at 200 Hz Xc= 1/(2π x F x C) or Xc= 1/(6.28 x .0002 x 1) or Xc= 796 Ω Find the Capacitive reactance of a 10 PF capacitor at 7 MHz Xc= 1/(2π x F x C) or Xc= 1/(6.28 x 7.0 x 10 ^-6 ) or Xc= 2,275 Ω The AC resistance of an Inductor is called Inductive reactance (XL) and is calculated using the formula: XL= 2π x F x L with L in µH and F in MHz Examples: Find the inductive reactance of a 1 µH inductor at 100 MHz XL= 2π x F x L or XL= 6.28 x 100 x 1 or XL= 628 Ω Find the inductive reactance of a 100 µH inductor at 7 MHz XL= 2π x F x L or XL= 6.28 x 7 x 100 or XL= 4,396 Ω Circuit Impedance The term Impedance refers to the equivalent circuit resistance in ohms for a circuit consisting of resistance and capacitive reactance and / or inductive reactance. To solve these problems for series circuits we use a rectangular coordinate graph and basic algebra and trigonometry. When working with complex circuits containing resistance and reactance, the reactive components are shown with a lower case j prefix. Inductive reactance is shown with a +j prefix and capacitive reactance with a –j prefix. Rectangular Coordinate System When solving problems involving impedance and phase angle of AC series circuits we show the circuit element values in a rectangular format. The rectangular format consists of a horizontal line intersected at 90° by a vertical line. Values on the horizontal or X axis are positive to the right of the vertical line and negative to the left. Values on the vertical or Y axis are positive above the X axis and Negative below the X axis. E5B07 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms? 14.0 degrees with the voltage lagging the current Tangent of θ = Y / X or Tangent of θ = 250 / 1000 or Tangent of θ = .25 or θ = 14.04° E5B08 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 100 ohms, R is 100 ohms, and XL is 75 ohms? 14 degrees with the voltage lagging the current Rev 2.00 Page 46 AD7FO’s 2012-2016 Extra Class Syllabus Tangent of θ = Y / X or Tangent of θ = (75-100)/100 or Tangent of θ = -.25 or θ = -14.04° Rules for calculating impedances and phase angles 1. Impedances in series add together 2. Admittance is the reciprocal of Impedance (admittance = 1/impedance) 3. Admittances in parallel add together 4. Inductive and capacitive reactance in series cancel 5. 1/j is equal to – j E5B09 What is the relationship between the current through a capacitor and the voltage across a capacitor? Current leads voltage by 90 degrees E5B10 What is the relationship between the current through an inductor and the voltage across an inductor? Voltage leads current by 90 degrees E5B11 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 50 ohms? 14 degrees with the voltage leading the current Tangent of θ = Y / X or Tangent of θ = (50-25)/100 or Tangent of θ = -.25 or θ = 14.04° E5B12 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 75 ohms, R is 100 ohms, and XL is 50 ohms? 14 degrees with the voltage lagging the current Tangent of θ = Y / X or Tangent of θ = (50-75)/100 or Tangent of θ = -.25 or θ = -14.04° E5B13 What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 250 ohms, R is 1 kilohm, and XL is 500 ohms? 14.04 degrees with the voltage leading the current Tangent of θ = Y/X or Tangent of θ = (XL - XC)/I Rev 2.00 or θ = (500-250)/1000 or Tangent of θ = 0.25 or θ = 14.036° Page 47 AD7FO’s 2012-2016 Extra Class Syllabus E5C Impedance plots and coordinate systems: plotting impedances in polar coordinates; rectangular coordinates E5C01 In polar coordinates, what is the impedance of a network consisting of a 100-ohm-reactance inductor in series with a 100-ohm resistor? 141 ohms at an angle of 45 degrees Z= √(X² + Y²) or Z= √(100² + 100²) or Z= √( 20,000) or Z= 141.42 Ω θ = arc tan (reactance/resistance) or arc tan 100/100 or arc tan 1 or 45° j 100 100 Ω E5C02 In polar coordinates, what is the impedance of a network consisting of a 100-ohm-reactance inductor, a 100-ohm-reactance capacitor, and a 100-ohm resistor, all connected in series? 100 ohms at an angle of 0 degrees Z= √( R² + (XL –Xc)²) or Z= √( 100² + (100-100)²) or Z= √( 10,000) or Z= 100 Ω θ = arc tan (reactance/resistance) or arc tan 0/100 or arc tan 0 or 0° Note- the Y side is the vector sum of the inductive reactance and capacitive reactance or (XL –Xc) j 100 100 Ω -j 100 E5C03 In polar coordinates, what is the impedance of a network consisting of a 300-ohm-reactance capacitor, a 600-ohm-reactance inductor, and a 400-ohm resistor, all connected in series? 500 ohms at an angle of 37 degrees Z= √(R² + (XL –Xc)²) or Z= √( 400² + (600-300)²) or Z= √( 250,000) or Z= 500 Ω Rev 2.00 Page 48 AD7FO’s 2012-2016 Extra Class Syllabus θ = arc tan (reactance/resistance) or 300/400 or arc tan .75 or 36.9° j 600 -j300 400Ω E5C04 In polar coordinates, what is the impedance of a network consisting of a 400-ohm-reactance capacitor in series with a 300-ohm resistor? D. 500 ohms at an angle of -53.1 degrees Z= √(X² + (XL –Xc)²) or Z= √( 300² + (0-400)²) or Z= √(250,000) or Z= 500 Ω θ = arc tan (reactance/resistance) or arc tan (-400/300) or arc tan (0/100 or arc tan (- 1.33) or -53.13° 300Ω -j400 E5C05 In polar coordinates, what is the impedance of a network consisting of a 400-ohm-reactance inductor in parallel with a 300ohm resistor? 240 ohms at an angle of 36.9 degrees Impedance (Z) = (R x XL) / √ (R² +XL² ) = (300 x 400) / √ (300² +400²) = 120,000 / 500 = 240 Ω θ = arctan 1/ (Reactance/Resistance) or θ= arctan 1/ (400 / 300) or θ= arctan 1/ 1.333 or arctan =.750 or θ =36.87° E5C06 In polar coordinates, what is the impedance of a network consisting of a 100-ohm-reactance capacitor in series with a 100-ohm resistor? 141 ohms at an angle of -45 degrees Z= √(X² + (XL –Xc)²) or Z= √( 100² + (-100)²) or Z= √(20,000) or Z= 141.4 Ω Angle is arctan 1/ (reactance/resistance) or arctan 1/ (100/100) or arc tan (- 1) or -45° Rev 2.00 Page 49 AD7FO’s 2012-2016 Extra Class Syllabus E5C07 In polar coordinates, what is the impedance of a network comprised of a 100-ohm-reactance capacitor in parallel with a 100ohm resistor? 71 ohms at an angle of -45 degrees Admittance = 1/100 +(-j/100) or 0.01 +j 0.01 Angle =arc tan .01/.01 or 45° (-45° in polar coordinates) Impedance = 1/ (√ ( (.01)² x (.01)² )) or 1/(.0141) or 70.71 Ώ E5C08 In polar coordinates, what is the impedance of a network comprised of a 300-ohm-reactance inductor in series with a 400-ohm resistor? 500 ohms at an angle of 37 degrees Z= √(X² + (XL –Xc)²) or Z= √( 400² + (0-300)²) or Z= √(250,000) or Z= 500 Ω Angle is arc tan (reactance/resistance) or arc tan (300/400) or arc tan (.75) or 36.86° j300 400Ω - E5C09 When using rectangular coordinates to graph the impedance of a circuit, what does the horizontal axis represent? Resistive component E5C10 When using rectangular coordinates to graph the impedance of a circuit, what does the vertical axis represent? Reactive component E5C11 What do the two numbers represent that are used to define a point on a graph using rectangular coordinates? The coordinate values along the horizontal and vertical axes E5C12 If you plot the impedance of a circuit using the rectangular coordinate system and find the impedance point falls on the right side of the graph on the horizontal axis, what do you know about the circuit? It is equivalent to a pure resistance E5C13 What coordinate system is often used to display the resistive, inductive, and/or capacitive reactance components of an impedance? Rectangular coordinates E5C14 What coordinate system is often used to display the phase angle of a circuit containing resistance, inductive and/or capacitive reactance? Polar coordinates Rev 2.00 Page 50 AD7FO’s 2012-2016 Extra Class Syllabus E5C15 In polar coordinates, what is the impedance of a circuit of 100 -j100 ohms impedance? 141 ohms at an angle of -45 degrees Z= √(X² + (XL –Xc)²) or Z= √( 100² + ( -100)²) or Z= √(20,000) or Z= 141.42 Ω Angle is arc tan (reactance/resistance) or arc tan (-100/100) or arc tan (-1) or -45° Parallel circuit solutions Tutorial Solving for parallel circuits for ac circuits is similar to the way we solved resistance parallel circuits. Remember the Equation: R(total) = 1 / ((1/R1) +(1/R2) +(1/R3)) The solution involved finding the conductance (G) of each leg by dividing the resistances into 1 and summing them. This gave the total circuit conductance in Siemens. The Mho was the term previously used for Seimen. G = (1/R1) +(1/R2) +(1/R3) To find the resistance we divided the conductance into 1 and ended up with the parallel circuit resistance. Susceptance We do the same thing to find the impedance of parallel ac circuits. The names of the circuit references change- Impedance becomes admittance, “Y”, (1/impedance). Resistance becomes conductance, “G”, (1/resistance) and susceptance , “B” (1/reactance) We start by finding the “conductance of the resistive and reactive components and just add them as we did in the resistance solution (remember we will be summing resistive (real) and reactive (imaginary) conductance. The rectangular coordinates for parallel circuit solutions are shown below. Note that the reactive axis direction is opposite that of the series circuit solutions in that that reactive conductance is + for capacity and – for inductance. E5C16 In polar coordinates, what is the impedance of a circuit that has an admittance of 7.09 millisiemens at 45 degrees? 141 ohms at an angle of -45 degrees Polar Impedance (Z) =1/admittance or Z= 1/.00709 or Z= 141.04Ω Polar angle = 1 / j (admittance angle) = 1/j(45°) or -j45° E5C17 In rectangular coordinates, what is the impedance of a circuit that has an admittance of 5 millisiemens at -30 degrees? 173 +j100 ohms Polar Impedance (Z) =1/admittance or Z= 1/.005 or Z= 200Ω Polar angle = 1/amdittance angle = 1/- 30° or +30° Cos θ= resistance (R) / Impedance (Z) or R = 200Ω x Cosine 30° or R = 200Ω x .866 or 173.2 Ω Sin θ= reactance (j) / Impedance (Z) or j = 200 x Sine 30° or j = 200Ω x .50 or j100Ω Rev 2.00 Page 51 AD7FO’s 2012-2016 Extra Class Syllabus E5C18 In polar coordinates, what is the impedance of a series circuit consisting of a resistance of 4 ohms, an inductive reactance of 4 ohms, and a capacitive reactance of 1 ohm? 5 ohms at an angle of 37 degrees R=400 Ω Xc= 1/ (2 π FC) or Xc= 1/(6.28 x 14 x .000038) or Xc= -300 Ω (remember capacitive reactance is negative). Figure E5-2 Point 3 Point 2 Point 8 Point 5 Point 6 Point 4 Point 7 Point 1 E5C19 Which point on Figure E5-2 best represents that impedance of a series circuit consisting of a 400 ohm resistor and a 38 picofarad capacitor at 14 MHz? Point 4 R=400 Ω Xc= 1/ (2 π FC) or Xc= 1/(6.28 x 14 x .000038) or Xc= -300 Ω (remember capacitive reactance is negative). E5C20 Which point in Figure E5-2 best represents the impedance of a series circuit consisting of a 300 ohm resistor and an 18 microhenry inductor at 3.505 MHz? Point 3 R=300 Ω XL= (2 π FL) or XL = (6.28 x 3.505 x 18) or XL = 396.4 Ω (remember inductive reactance is positive) Answer is 300 Ω + j 395 Ω E5C21 Which point on Figure E5-2 best represents the impedance of a series circuit consisting of a 300 ohm resistor and a 19 picofarad capacitor at 21.200 MHz? Point 1 E5C22 In rectangular coordinates, what is the impedance of a network consisting of a 10-microhenry inductor in series with a 40-ohm resistor at 500 MHz? 40 + j31,400 R=40 Ω XL= (2 π F x L) or XL = (6.28 x 500 x 10) or XL = 31,416 Ω (remember inductive reactance is positive) Answer is 40 Ω + j 31,400 Rev 2.00 Page 52 AD7FO’s 2012-2016 Extra Class Syllabus E5C23 Which point on Figure E5-2 best represents the impedance of a series circuit consisting of a 300-ohm resistor, a 0.64microhenry inductor and an 85-picofarad capacitor at 24.900 MHz? Point 8 R=300 Ω Xc= 1/ (2 π F x C) or Xc= 1/(6.28 x 24.9 x .000085) or Xc= -75.19 Ω (remember capacitive reactance is negative) XL= (2 π FL) or XL = (6.28 x 24.9 x .64) or XL = 100.12 Ω (remember inductive reactance is positive) Net reactance is the sum of Xc and XL or -75.19 + 100.12 or +24.9 Answer is 300 Ω + j 24.9 E5D AC and RF energy in real circuits: skin effect; electrostatic and electromagnetic fields; reactive power; power factor; coordinate systems E5D01 What is the result of skin effect? As frequency increases, RF current flows in a thinner layer of the conductor, closer to the surface DC RF UHF Current flow in cross section of a conductor E5D02 Why is the resistance of a conductor different for RF currents than for direct currents? Because of skin effect E5D03 What device is used to store electrical energy in an electrostatic field? A capacitor E5D04 What unit measures electrical energy stored in an electrostatic field? Joule A Joule is defined as a quantity of energy equal to one Newton of force acting over 1 meter. The newton is the SI unit for force; it is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one meter per second squared. E5D05 Which of the following creates a magnetic field? Electric current Rev 2.00 Page 53 AD7FO’s 2012-2016 Extra Class Syllabus E5D06 In what direction is the magnetic field oriented about a conductor in relation to the direction of electron flow? In a direction determined by the left-hand rule The Left Hand Rule shows what happens when charged particles (such as electrons in a current) enter a magnetic field. You need to contort your hand in an unnatural position for this rule, illustrated below. As you can see, if your index finger points in the direction of a magnetic field, and your middle finger, at a 90 degree angle to your index, points in the direction of the charged particle (as in an electrical current), then your extended thumb (forming an L with your index) points in the direction of the force exerted upon that particle. This rule is also called Fleming's Left Hand Rule, after English electronics pioneer John Ambrose Fleming, who came up with it. E5D07 What determines the strength of a magnetic field around a conductor? The amount of current E5D08 What type of energy is stored in an electromagnetic or electrostatic field? Potential energy E5D09 What happens to reactive power in an AC circuit that has both ideal inductors and ideal capacitors? It is repeatedly exchanged between the associated magnetic and electric fields, but is not dissipated E5D10 How can the true power be determined in an AC circuit where the voltage and current are out of phase? By multiplying the apparent power times the power factor Understanding the Power Factor explanation The components of motor (or other inductive load) current are load current and magnetizing current (adding those instantaneous values yields the total circuit current). Also, because load current is in phase with voltage and magnetizing current lags voltage by 90 degrees, their sum will be a sine wave that peaks somewhere between 0 and 90 degrees lagging which is the inductive current's offset (in time) from voltage. There are negative effects associated with increased offset and that’s part of the power factor explanation. Power Factor represents the offset in time between voltage and the total current and is defined as the cosine of that offset. So when you look at the example in the graphic below, Total Current lags the voltage by 45 degrees. That is the offset. The cosine of 45 degrees is 0.707, and we call it "lagging" because the current lags behind the voltage Rev 2.00 Page 54 AD7FO’s 2012-2016 Extra Class Syllabus If the offset was 0 degrees (voltage and current in phase), the power factor would be 1.0 (cosine 0 = 1) and if the offset were a full 90 degrees (this would be all magnetizing current), the power factor would be 0.0 (cosine 90 = 0). So big deal....why is this offset so important? In a motor (or Inductive load), the component of load current is the current associated with doing work (i.e. pumping fluid, compressing gas, running your Kilowatt rig, etc.) and the magnetizing current is not doing work. I know without the magnetic field the things like motors wouldn't work. This is true, however, as stated earlier; the magnetic field takes some energy to get built up in one half cycle and then returns that energy to the system in the next half cycle, so its net effect is that it uses no energy. But if we consider the cable that delivers power to the circuit; when we add the magnetizing current to the load current, the cable's total current flow becomes larger. We, however, really just want to drive the load. If we could find a way to supply the magnetizing current without sending it down the cable, then the cable would only need to deliver the load current. This can be done by adding a capacitor across the inductive load which stores and releases energy for use by the inductive load locally at the motor-end of the cable delivering power. E5D11 What is the power factor of an R-L circuit having a 60 degree phase angle between the voltage and the current? 0.5 PF is the cosine function of the voltage to current angle ►PF =cosine of 60° or PF= 0.5 E5D12 How many watts are consumed in a circuit having a power factor of 0.2 if the input is 100-V AC at 4 amperes? 80 watts Power Consumed = V x I x PF or 100 x 4 x .2 or 80 watts E5D13 How much power is consumed in a circuit consisting of a 100 ohm resistor in series with a 100 ohm inductive reactance drawing 1 ampere? 100 Watts Power(real) = I² x R or Power(real) = (1)² x 100 or 100 watts. (Only the circuit resistance consumes power) E5D14 What is reactive power? Wattless, nonproductive power E5D15 What is the power factor of an RL circuit having a 45 degree phase angle between the voltage and the current? 0.707 PF = Cosine of 45° or PF = 0.707 E5D16 What is the power factor of an RL circuit having a 30 degree phase angle between the voltage and the current? 0.866 Rev 2.00 Page 55 AD7FO’s 2012-2016 Extra Class Syllabus PF Cosine of 30° or PF = 0.866 E5D17 How many watts are consumed in a circuit having a power factor of 0.6 if the input is 200V AC at 5 amperes? 600 watts Power Consumed = V x I x PF or 200 x 5 x .6 or 600 watts E5D18 How many watts are consumed in a circuit having a power factor of 0.71 if the apparent power is 500 VA? 355 W Power Consumed = Apparent power x PF or 500 x .71 or 355 watts Rev 2.00 Page 56 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E6 - CIRCUIT COMPONENTS [6 Exam Questions - 6 Groups] E6A Semiconductor materials and devices: semiconductor materials; germanium, silicon, P-type, N-type; transistor types: NPN, PNP, junction, field-effect transistors: enhancement mode; depletion mode; MOS; CMOS; N-channel; P-channel Transistor Construction E6A01 In what application is gallium arsenide used as a semiconductor material in preference to germanium or silicon? At microwave frequencies E6A02 Which of the following semiconductor materials contains excess free electrons? N-type E6A03 What are the majority charge carriers in P-type semiconductor material? Holes E6A04 What is the name given to an impurity atom that adds holes to a semiconductor crystal structure? Acceptor impurity E6A05 What is the alpha of a bipolar junction transistor? The change of collector current with respect to emitter current E6A06 What is the beta of a bipolar junction transistor? The change in collector current with respect to base current Figure E6-1 Rev 2.00 1 2 3 4 5 6 Page 57 AD7FO’s 2012-2016 Extra Class Syllabus E6A07 In Figure E6-1, what is the schematic symbol for a PNP transistor? 1 (one) E6A08 What term indicates the frequency at which the grounded-base current gain of a transistor has decreased to 0.7 of the gain obtainable at 1 kHz? Alpha cutoff frequency E6A09 What is a depletion-mode FET? An FET that exhibits a current flow between source and drain when no gate voltage is applied Figure E6-2 E6A10 In Figure E6-2, what is the schematic symbol for an N-channel dual-gate MOSFET? 4 (four) E6A11 In Figure E6-2, what is the schematic symbol for a P-channel junction FET? 1 (one) E6A12 Why do many MOSFET devices have internally connected Zener diodes on the gates? To reduce the chance of the gate insulation being punctured by static discharges or excessive voltages E6A13 What do the initials CMOS stand for? Complementary Metal-Oxide Semiconductor E6A14 How does DC input impedance at the gate of a field-effect transistor compare with the DC input impedance of a bipolar transistor? An FET has high input impedance; a bipolar transistor has low input impedance E6A15 Which of the following semiconductor materials contains an excess of holes in the outer shell of electrons? P-type E6A16 What are the majority charge carriers in N-type semiconductor material? Free electrons E6A17 What are the names of the three terminals of a field-effect transistor? Gate, drain, source E6B Semiconductor diodes Rev 2.00 Page 58 AD7FO’s 2012-2016 Extra Class Syllabus E6B01 What is the most useful characteristic of a Zener diode? A constant voltage drop under conditions of varying current The Zener diode symbol is number 3 in figure E6-3. Once the Zener voltage is reached increasing +VI will not cause Vo to increase only the current will increase creating a larger voltage drop across R, up to the maximum current rating for the Zener diode. E6B02 What is an important characteristic of a Schottky diode as compared to an ordinary silicon diode when used as a power supply rectifier? Less forward voltage drop The Schottky diode or Schottky barrier diode is an electronic component that is widely used for radio frequency (RF) application as a mixer or detector diode. The Schottky diode is also used in power applications as a rectifier because of its low forward voltage drop. Although normally called the Schottky diode these days it is also sometimes referred to as the surface barrier diode, hot carrier or even electron diode. E6B03 What special type of diode is capable of both amplification and oscillation? Tunnel Diode The tunnel diode symbol is number 2 in figure E6-3. Figure E6-3 1 2 5 6 3 7 4 8 E6B04 What type of semiconductor device is designed for use as a voltage-controlled capacitor? Varactor diode The Varactor diode symbol is number 1 in figure E6-3 and as shown to the right of the graphic below. Rev 2.00 Page 59 AD7FO’s 2012-2016 Extra Class Syllabus E6B05 What characteristic of a PIN diode makes it useful as an RF switch or attenuator? A large region of intrinsic material E6B06 Which of the following is a common use of a hot-carrier diode? As a VHF / UHF mixer or detector E6B07 What is the failure mechanism when a junction diode fails due to excessive current? Excessive junction temperature E6B08 Which of the following describes a type of semiconductor diode? Metal-semiconductor junction E6B09 What is a common use for point contact diodes? As an RF detector E6B10 In Figure E6-3, what is the schematic symbol for a light-emitting diode? 5 (five) E6B11 What is used to control the attenuation of RF signals by a PIN diode? Forward DC bias current E6B12 What is one common use for PIN diodes? As an RF switch E6B13 What type of bias is required for an LED to emit light? Forward bias E6C Integrated circuits: TTL digital integrated circuits; CMOS digital integrated circuits; gates E6C01 What is the recommended power supply voltage for TTL series integrated circuits? 5 volts E6C02 What logic state do the inputs of a TTL device assume if they are left open? A logic-high state E6C03 Which of the following describes tri-state logic? Logic devices with 0, 1, and high impedance output states E6C04 Which of the following is the primary advantage of tri-state logic? Ability to connect many device outputs to a common bus E6C05 Rev 2.00 Page 60 AD7FO’s 2012-2016 Extra Class Syllabus Which of the following is an advantage of CMOS logic devices over TTL devices? Lower power consumption E6C06 Why do CMOS digital integrated circuits have high immunity to noise on the input signal or power supply? The input switching threshold is about one-half the power supply voltage Figure E6-5 1 2 3 4 5 6 E6C07 In Figure E6-5, what is the schematic symbol for an AND gate? 1(one) If inputs A and B are 1 then the output is 1. Input A Input B output 0 0 0 0 1 0 1 0 0 1 1 1 E6C08 In Figure E6-5, what is the schematic symbol for a NAND gate? 2 (two) If not A and B are 1 then the output is 1. Input A Input B output 0 0 1 0 1 1 1 0 1 1 1 0 E6C09 In Figure E6-5, what is the schematic symbol for an OR gate? 3 (three) If either A or B input are 1 then the output is 1. Input A Input B output 0 0 0 0 1 1 1 0 1 1 1 1 E6C10 In Figure E6-5, what is the schematic symbol for a NOR gate? 4 (four) Rev 2.00 Page 61 AD7FO’s 2012-2016 Extra Class Syllabus If neither A or B are 1 then the output will be 1. Input A Input B output 0 0 1 0 1 0 1 0 0 1 1 0 E6C11 In Figure E6-5, what is the schematic symbol for the NOT operation (inverter)? 5 (five) If the input is high the output is low, if the input is low the output will be high. Input 0 1 Output 1 0 E6C12 What is BiCMOS logic? An integrated circuit logic family using both bipolar and CMOS transistors E6C13 Which of the following is an advantage of BiCMOS logic? It has the high input impedance of CMOS and the low output impedance of bipolar transistors E6D Optical devices and toroids: cathode-ray tube devices; charge-coupled devices (CCDs); liquid crystal displays (LCDs) Toroids: permeability; core material; selecting; winding E6D01 What is cathode ray tube (CRT) persistence? The length of time the image remains on the screen after the beam is turned off E6D02 Exceeding what design rating can cause a cathode ray tube (CRT) to generate X-rays? The anode voltage E6D03 Which of the following is true of a charge-coupled device (CCD)? It samples an analog signal and passes it in stages from the input to the output E6D04 What function does a charge-coupled device (CCD) serve in a modern video camera? It stores photogenerated charges as signals corresponding to pixels E6D05 What is a liquid-crystal display (LCD)? A display using a crystalline liquid which, in conjunction with polarizing filters, becomes opaque when voltage is applied E6D06 What core material property determines the inductance of a toroidal inductor? Permeability E6D07 What is the usable frequency range of inductors that use toroidal cores, assuming a correct selection of core material for the frequency being used? From less than 20 Hz to approximately 300 MHz Rev 2.00 Page 62 AD7FO’s 2012-2016 Extra Class Syllabus E6D08 What is one important reason for using powdered-iron toroids rather than ferrite toroids in an inductor? Powdered-iron toroids generally maintain their characteristics at higher currents E6D09 What devices are commonly used as VHF and UHF parasitic suppressors at the input and output terminals of transistorized HF amplifiers? Ferrite beads E6D10 What is a primary advantage of using a toroidal core instead of a solenoidal core in an inductor? Toroidal cores confine most of the magnetic field within the core material Applications for powdered Iron toroids would be oscillator and filter circuits where inductance stability with temperature is important. E6D11 How many turns will be required to produce a 1-mH inductor using a ferrite toroidal core that has an inductance index (A L) value of 523 millihenrys/1000 turns? 43 turns N turns = 1000 x (√ (L / AL)) or N turns = 1000 x (√ (1 / 523)) or 43.7 turns E6D12 How many turns will be required to produce a 5-microhenry inductor using a powdered-iron toroidal core that has an inductance index (A L) value of 40 microhenrys/100 turns? 35 turns N turns = 100 x (√ (L / AL)) or N turns = 100 x (√ (5 / 40)) or 35.35 turns E6D13 What type of CRT deflection is better when high-frequency waveforms are to be displayed on the screen? Electrostatic E6D14 Which is NOT true of a charge-coupled device (CCD)? It is commonly used as an analog-to-digital converter E6D15 What is the principle advantage of liquid-crystal display (LCD) devices over other types of display devices? They consume less power E6D16 What is one reason for using ferrite toroids rather than powdered-iron toroids in an inductor? Ferrite toroids generally require fewer turns to produce a given inductance value Rev 2.00 Page 63 AD7FO’s 2012-2016 Extra Class Syllabus E6E Piezoelectric crystals and MMICs: quartz crystal oscillators and crystal filters); monolithic amplifiers E6E01 What is a crystal lattice filter? A filter with narrow bandwidth and steep skirts made using quartz crystals E6E02 Which of the following factors has the greatest effect in helping determine the bandwidth and response shape of a crystal ladder filter? The relative frequencies of the individual crystals E6E03 What is one aspect of the piezoelectric effect? Physical deformation of a crystal by the application of a voltage E6E04 What is the most common input and output impedance of circuits that use MMICs? 50 ohms E6E05 Which of the following noise figure values is typical of a low-noise UHF preamplifier? 2 dB E6E06 What characteristics of the MMIC make it a popular choice for VHF through microwave circuits? Controlled gain, low noise figure, and constant input and output impedance over the specified frequency range E6E07 Which of the following is typically used to construct a MMIC-based microwave amplifier? Microstrip construction Rev 2.00 Page 64 AD7FO’s 2012-2016 Extra Class Syllabus E6E08 How is power-supply voltage normally furnished to the most common type of monolithic microwave integrated circuit (MMIC)? Through a resistor and/or RF choke connected to the amplifier output lead E6E09 Which of the following must be done to insure that a crystal oscillator provides the frequency specified by the crystal manufacturer? Provide the crystal with a specified parallel capacitance E6E10 THIS QUESTION HAS BEEN REMOVED FROM THE QUESTION POOL What is the equivalent circuit of a quartz crystal? Motional capacitance, motional inductance and loss resistance in series, with a shunt capacitance representing electrode and stray capacitance E6E11 Which of the following materials is likely to provide the highest frequency of operation when used in MMICs? Gallium nitride E6E12 What is a "Jones filter" as used as part of a HF receiver IF stage? A variable bandwidth crystal lattice filter Rev 2.00 Page 65 AD7FO’s 2012-2016 Extra Class Syllabus E6F Optical components and power systems: photoconductive principles and effects, photovoltaic systems, optical couplers, optical sensors, and optoisolators E6F01 What is photoconductivity? The increased conductivity of an illuminated semiconductor In other words the resistance decreases when light shines on it E6F02 What happens to the conductivity of a photoconductive material when light shines on it? It increases In other words the resistance decreases E6F03 What is the most common configuration of an optoisolator or optocoupler? An LED and a phototransistor E6F04 What is the photovoltaic effect? The conversion of light to electrical energy E6F05 Which of the following describes an optical shaft encoder? A device which detects rotation of a control by interrupting a light source with a patterned wheel E6F06 Which of these materials is affected the most by photoconductivity? A crystalline semiconductor E6F07 What is a solid state relay? A device that uses semiconductor devices to implement the functions of an electromechanical relay E6F08 Why are optoisolators often used in conjunction with solid state circuits when switching 120 VAC? Optoisolators provide a very high degree of electrical isolation between a control circuit and the circuit being switched Rev 2.00 Page 66 AD7FO’s 2012-2016 Extra Class Syllabus E6F09 What is the efficiency of a photovoltaic cell? The relative fraction of light that is converted to current E6F10 What is the most common type of photovoltaic cell used for electrical power generation? Silicon E6F11 Which of the following is the approximate open-circuit voltage produced by a fully-illuminated silicon photovoltaic cell? 0.5 V Twenty seven cells would be required to produce 13.5 volts for charging a 12 volt battery. E6F12 What absorbs the energy from light falling on a photovoltaic cell? Electrons Rev 2.00 Page 67 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E7 - PRACTICAL CIRCUITS [8 Exam Questions - 8 Groups] E7A Digital circuits: digital circuit principles and logic circuits: classes of logic elements; positive and negative logic; frequency dividers; truth tables E7A01 Which of the following is a bistable circuit? A flip-flop E7A02 How many output level changes are obtained for every two trigger pulses applied to the input of a T flip-flop circuit? Two Input Output E7A03 Which of the following can divide the frequency of a pulse train by 2? A flip-flop E7A04 How many flip-flops are required to divide a signal frequency by 4? 2 (two) Output 50 KHz Output 25 KHz Output 12.5 KHz Input 100 KHz E7A05 Which of the following is a circuit that continuously alternates between two states without an external clock? Astable multivibrator E7A06 What is a characteristic of a monostable multivibrator? It switches momentarily to the opposite binary state and then returns, after a set time, to its original state Rev 2.00 Page 68 AD7FO’s 2012-2016 Extra Class Syllabus E7A07 What logical operation does a NAND gate perform? It produces a logic "0" at its output only when all inputs are logic "1" Input A 0 0 1 1 Input B output 0 1 1 1 0 1 1 0 E7A08 What logical operation does an OR gate perform? It produces a logic "1" at its output if any or all inputs are logic "1" Input A 0 0 1 1 Input B output 0 0 1 1 0 1 1 1 E7A09 What logical operation is performed by a two-input exclusive NOR gate? It produces a logic "0" at its output if any single input is a logic “1” Input A 0 0 1 1 Input B output 0 1 1 0 0 0 1 1 E7A10 What is a truth table? A list of inputs and corresponding outputs for a digital device Input A 0 0 1 1 Input B output 0 1 1 0 0 0 1 0 E7A11 What is the name for logic which represents a logic "1" as a high voltage? Positive Logic E7A12 What is the name for logic which represents a logic "0" as a high voltage? Negative logic E7A13 What is an SR or RS flip-flop? A set/reset flip-flop whose output is low when R is high and S is low, high when S is high and R is low, and unchanged when both inputs are low Rev 2.00 Page 69 AD7FO’s 2012-2016 Extra Class Syllabus E7A14 What is a JK flip-flop? A flip-flop similar to an RS except that it toggles when both J and K are high E7A15 (What is a D flip-flop? A flip-flop whose output takes on the state of the D input when the clock signal transitions from low to high. E7B Amplifiers: Class of operation; vacuum tube and solid-state circuits; distortion and intermodulation; spurious and parasitic suppression; microwave amplifiers Amplifier classes: Power amplifiers are classified primarily by the design of the output stage. Classification is based on the amount of time the output device(s) operate during each cycle of the input signal. Class A operation is where the tube conducts continuously for the entire cycle of the input signal, or a bias current flows in the output devices at all times. The key ingredient of class A operation is that the output is always on. Conversely the output device is never turned off. Because of this, class A amplifiers are single-ended designs. Class A is the most inefficient of all power amplifier designs, averaging only around 20%. Because of this, class A amplifiers are large, heavy and run very hot. On the positive side, class A designs are inherently the most linear, and have the least amount of distortion. When driving an A class amplifier care should be taken to insure the peak to peak input voltage stays within the linear range of the amplifier. Class B has conduction occurring for only for ½ of the input cycle. Class B amplifiers typically have dual output devices operating 180º out of phase with each other in a push / pull configuration to allow the full cycle of the input to be amplified. Both output devices are never allowed to be on at the same time, bias is set so that current flow in a specific output device is zero without an input signal. Current only flows in each of the push / pull amplifier output amplifiers for one half cycle. Thus each output amplifier is only on for ½ of a complete sinusoidal signal cycle. Class B push pull designs show high efficiency but poor linearity around the 0 voltage crossover region. This is due to the time it takes to turn one device off and the other device on, which translates into extreme crossover distortion. Thus restricting class B designs to power consumption critical applications, e.g., battery operated equipment. Class B push / pull transmitter power amplifiers reduce or prevent even order harmonics in the output signal. Class AB operation allows both devices to be on at the same time (like in class A), but just barely. The output bias is set so that current flows in a specific output device appreciably more than a half cycle but less than the entire cycle. That is, only a small amount of current is allowed to flow through both devices, unlike the complete load current of class A designs, but enough to keep each device operating so they respond instantly to input voltage demands. Thus the inherent non-linearity of class B designs is eliminated, without the gross inefficiencies of the class A design. It is this combination of good efficiency (around 50%) with excellent linearity that makes class AB the most popular audio amplifier design. Class C operation allows current flows for less than one half cycle of the input signal. The class C operation is achieved by reverse biasing the amplifier to point below cutoff and allows only the portion of the input signal that overcomes the reverse Rev 2.00 Page 70 AD7FO’s 2012-2016 Extra Class Syllabus bias to cause current flow. The class C operated amplifier is used as a radio-frequency amplifier in frequency modulated or CW transmitters. E7B01 For what portion of a signal cycle does a Class AB amplifier operate? More than 180 degrees but less than 360 degrees E7B02 What is a Class D amplifier? A type of amplifier that uses switching technology to achieve high efficiency E7B03 Which of the following forms the output of a class D amplifier circuit? A low-pass filter to remove switching signal components E7B04 Where on the load line of a Class A common emitter amplifier would bias normally be set? Approximately half-way between saturation and cutoff E7B05 What can be done to prevent unwanted oscillations in an RF power amplifier? Install parasitic suppressors and/or neutralize the stage E7B06 Which of the following amplifier types reduces or eliminates even-order harmonics? Push-pull E7B07 Which of the following is a likely result when a Class C amplifier is used to amplify a single-sideband phone signal? Signal distortion and excessive bandwidth E7B08 How can an RF power amplifier be neutralized? By feeding a 180-degree out-of-phase portion of the output back to the input E7B09 Which of the following describes how the loading and tuning capacitors are to be adjusted when tuning a vacuum tube RF power amplifier that employs a pi-network output circuit? The tuning capacitor is adjusted for minimum plate current, while the loading capacitor is adjusted for maximum permissible plate current Rev 2.00 Page 71 AD7FO’s 2012-2016 Extra Class Syllabus Figure E7-1 E7B10 In Figure E7-1, what is the purpose of R1 and R2? Fixed bias Base Bias voltage point is set by the voltage division ratio of R1 and R2 based on the Vcc (+ in the schematic) E7B11 In Figure E7-1, what is the purpose of R3? Self -bias E7B12 What type of circuit is shown in Figure E7-1? Common emitter amplifier Figure E7-2 C1 C2 R E7B13 In Figure E7-2, what is the purpose of R? Emitter load E7B14 In Figure E7-2, what is the purpose of C2? Output coupling E7B15 What is one way to prevent thermal runaway in a bipolar transistor amplifier? Use a resistor in series with the emitter E7B16 What is the effect of intermodulation products in a linear power amplifier? Transmission of spurious signals E7B17 Why are third-order intermodulation distortion products of particular concern in linear power amplifiers? Because they are relatively close in frequency to the desired signal E7B18 Which of the following is a characteristic of a grounded-grid amplifier? Low input impedance Rev 2.00 Page 72 AD7FO’s 2012-2016 Extra Class Syllabus E7B19 What is a klystron? A VHF, UHF, or microwave vacuum tube that uses velocity modulation E7B20 What is a parametric amplifier? A low-noise VHF or UHF amplifier relying on varying reactance for amplification E7B21 Which of the following devices is generally best suited for UHF or microwave power amplifier applications? Field effect transistor The field-effect transistor (FET) is a transistor that relies on an electric field to control the shape and hence the conductivity of a channel of one type of charge carrier in a semiconductor material. E7C Filters and matching networks: types of networks; types of filters; filter applications; filter characteristics; impedance matching; DSP filtering E7C01 How are the capacitors and inductors of a low-pass filter Pi-network arranged between the network's input and output? A capacitor is connected between the input and ground, another capacitor is connected between the output and ground, and an inductor is connected between input and output E7C02 A T-network with series capacitors and a parallel shunt inductor has which of the following properties? It is a high-pass filter Rev 2.00 Page 73 AD7FO’s 2012-2016 Extra Class Syllabus E7C03 What advantage does a Pi-L-network have over a Pi-network for impedance matching between the final amplifier of a vacuumtube transmitter and an antenna? Greater harmonic suppression E7C04 How does an impedance-matching circuit transform a complex impedance to a resistive impedance? It cancels the reactive part of the impedance and changes the resistive part to a desired value E7C05 Which filter type is described as having ripple in the passband and a sharp cutoff? A Chebyshev filter E7C06 What are the distinguishing features of an elliptical filter? Extremely sharp cutoff with one or more notches in the stop band E7C07 What kind of filter would you use to attenuate an interfering carrier signal while receiving an SSB transmission? A notch filter E7C08 What kind of digital signal processing audio filter might be used to remove unwanted noise from a received SSB signal? An adaptive filter Rev 2.00 Page 74 AD7FO’s 2012-2016 Extra Class Syllabus An adaptive filter is a filter that self-adjusts its transfer function according to an optimization algorithm driven by an error signal. Because of the complexity of the optimization algorithms, most adaptive filters are digital filters. The adaptive filter uses feedback in the form of an error signal to refine its transfer function to match the changing parameters. E7C09 What type of digital signal processing filter might be used to generate an SSB signal? A Hilbert-transform filter The Hilbert transform is a linear operator in mathematics and in signal processing. E7C10 Which of the following filters would be the best choice for use in a 2 meter repeater duplexer? A cavity filter E7C11 Which of the following is the common name for a filter network which is equivalent to two L networks connected back-to-back with the inductors in series and the capacitors in shunt at the input and output? Pi E7C12 Which of the following describes a Pi-L network used for matching a vacuum-tube final amplifier to a 50-ohm unbalanced output? A Pi network with an additional series inductor on the output E7C13 What is one advantage of a Pi matching network over an L matching network consisting of a single inductor and a single capacitor? The Q of Pi networks can be varied depending on the component values chosen E7C14 Which of these modes is most affected by non-linear phase response in a receiver IF filter? Digital E7D Power supplies and voltage regulators E7D01 What is one characteristic of a linear electronic voltage regulator? The conduction of a control element is varied to maintain a constant output voltage Rev 2.00 Page 75 AD7FO’s 2012-2016 Extra Class Syllabus E7D02 What is one characteristic of a switching electronic voltage regulator? The control device’s duty cycle is controlled to produce a constant average output voltage E7D03 What device is typically used as a stable reference voltage in a linear voltage regulator? A Zener diode E7D04 Which of the following types of linear voltage regulator usually make the most efficient use of the primary power source? A series regulator E7D05 Which of the following types of linear voltage regulator places a constant load on the unregulated voltage source? A shunt regulator E7D06 What is the purpose of Q1 in the circuit shown in Figure E7-3? It increases the current-handling capability of the regulator Figure E7- 3 Q1 +25 C1 4000 +12 C3 0.01 R1 C2 4000 R2 D1 E7D07 What is the purpose of C2 in the circuit shown in Figure E7-3? It bypasses hum around D1 E7D08 What type of circuit is shown in Figure E7-3? Linear voltage regulator E7D09 What is the purpose of C1 in the circuit shown in Figure E7-3? It filters the supply voltage E7D10 What is the purpose of C3 in the circuit shown in Figure E7-3? It prevents self-oscillation E7D11 What is the purpose of R1 in the circuit shown in Figure E7-3? It supplies current to D1 Rev 2.00 Page 76 AD7FO’s 2012-2016 Extra Class Syllabus E7D12 What is the purpose of R2 in the circuit shown in Figure E7-3? It provides a constant minimum load for Q1 E7D13 What is the purpose of D1 in the circuit shown in Figure E7-3? To provide a voltage reference E7D14 What is one purpose of a "bleeder" resistor in a conventional (unregulated) power supply? To improve output voltage regulation E7D15 What is the purpose of a "step-start" circuit in a high-voltage power supply? To allow the filter capacitors to charge gradually This consists of inserting a resistor in the primary side of the transformer to limit the charge current on the capacitors at initial turn on. The series resistor is switched out after a few seconds of operation. E7D16 When several electrolytic filter capacitors are connected in series to increase the operating voltage of a power supply filter circuit, why should resistors be connected across each capacitor? A. To equalize, as much as possible, the voltage drop across each capacitor B. To provide a safety bleeder to discharge the capacitors when the supply is off C. To provide a minimum load current to reduce voltage excursions at light loads D. All of these choices are correct E7D17 What is the primary reason that a high-frequency inverter type high-voltage power supply can be both less expensive and lighter in weight than a conventional power supply? The high frequency inverter design uses much smaller transformers and filter components for an equivalent power output E7E Modulation and demodulation: reactance, phase and balanced modulators; detectors; mixer stages; DSP modulation and demodulation; software defined radio systems E7E01 Which of the following can be used to generate FM phone emissions? A reactance modulator on the oscillator E7E02 What is the function of a reactance modulator? To produce PM signals by using an electrically variable inductance or capacitance E7E03 How does an analog phase modulator function? By varying the tuning of an amplifier tank circuit to produce PM signals E7E04 What is one way a single-sideband phone signal can be generated? By using a balanced modulator followed by a filter A balanced mixer will output the sum and difference of the two signals applied (Carrier and SSB audio) and the carrier, suppressed by passing the modulator output through a filter so that the upper or lower sideband can be filtered leaving only one of the sideband signals. Rev 2.00 Page 77 AD7FO’s 2012-2016 Extra Class Syllabus E7E05 What circuit is added to an FM transmitter to boost the higher audio frequencies? A pre-emphasis network E7E06 Why is de-emphasis commonly used in FM communications receivers? For compatibility with transmitters using phase modulation E7E07 What is meant by the term baseband in radio communications? The frequency components present in the modulating signal E7E08 What are the principal frequencies that appear at the output of a mixer circuit? The two input frequencies along with their sum and difference frequencies If F1 is 10 MHz and F2 is 9 MHz the output from the mixer will be 1 MHz (the Difference) and 19 MHz (the sum). E7E09 What occurs when an excessive amount of signal energy reaches a mixer circuit? Spurious mixer products are generated E7E10 How does a diode detector function? By rectification and filtering of RF signals E7E11 Which of the following types of detector is well suited for demodulating SSB signals? Product detector E7E12 What is a frequency discriminator stage in a FM receiver? A circuit for detecting FM signals Rev 2.00 Page 78 AD7FO’s 2012-2016 Extra Class Syllabus E7E13 Which of the following describes a common means of generating an SSB signal when using digital signal processing? The quadrature method Quadrature modulation uses two data channels denoted I (in phase) and Q (quadrature phase) displaced by 90o with respect to each other. It may seem somewhat paradoxical, that although these two channels are combined prior to transmission, they do not interfere with each other. E7E14 What is meant by direct conversion when referring to a software defined receiver? Incoming RF is mixed to “baseband” for analog-to-digital conversion and subsequent processing The incoming signal is mixed with a signal at the same carrier frequency. The result will be a signal at twice the receive signal and another at zero frequency. This zero RF frequency will have only the modulation contained in the incoming signal and can be directly fed into an audio stage. E7F Frequency markers and counters: frequency divider circuits; frequency marker generators; frequency counters E7F01 What is the purpose of a prescaler circuit? It divides a higher frequency signal so a low-frequency counter can display the input frequency In a pre-scaled counter the input frequency would be divided by 10 or 100 or another multiple of 10. Therefore our counter that measures a non-pre-scaled frequency of 10 MHz with 1Hz of resolution would measure the same frequency in the ÷10 prescale mode with 10 Hz resolution using the same counter gate time. E7F02 Which of the following would be used to reduce a signal’s frequency by a factor of ten? Prescaler E7F03 What is the function of a decade counter digital IC? It produces one output pulse for every ten input pulses Rev 2.00 Page 79 AD7FO’s 2012-2016 Extra Class Syllabus A decade counter (divider) can be used as a prescaler for a counter (assuming it works high enough in frequency) to increase the counters frequency range by a factor of 10 (allowing a 10 MHz counter to have an extended frequency range to100 MHz). A circuit with 2 decade dividers in series would divide the input by 100, extending the range of our 10 MHz counter to 1,000 MHz E7F04 What additional circuitry must be added to a 100-kHz crystal-controlled marker generator so as to provide markers at 50 and 25 kHz? Two flip-flops E7F05 Which of the following is a technique for providing high stability oscillators needed for microwave transmission and reception? A. Use a GPS signal reference B. Use a rubidium stabilized reference oscillator C. Use a temperature-controlled high Q dielectric resonator D. All of these choices are correct E7F06 What is one purpose of a marker generator? To provide a means of calibrating a receiver's frequency settings E7F07 What determines the accuracy of a frequency counter? The accuracy of the time base E7F08 Which of the following is performed by a frequency counter? Counting the number of input pulses occurring within a specific period of time E7F09 What is the purpose of a frequency counter? To provide a digital representation of the frequency of a signal E7F10 What alternate method of determining frequency, other than by directly counting input pulses, is used by some counters? Period measurement plus mathematical computation A period measurement is the measurement of the time it takes for one or a number of cycles of the input signal and then converting the period measurement back to frequency. F = 1/ period for a 1 millisecond period the frequency would be F=1/.001 or F=1000 E7F11 What is an advantage of a period-measuring frequency counter over a direct-count type? It provides improved resolution of low-frequency signals within a comparable time period E7G Active filters and op-amps: active audio filters; characteristics; basic circuit design; operational amplifiers Rev 2.00 Page 80 AD7FO’s 2012-2016 Extra Class Syllabus Operational amplifier tutorial An operational amplifier, or op amp, is one of the most useful linear devices that have been developed with integrated circuitry. While it is possible to build an op amp with discrete components, the symmetry of this circuit requires a close match of many components and is more effective, and much easier, to implement in integrated circuitry. Fig E7-4 shows a basic op-amp circuit. The op amp approaches a perfect analog circuit building block. Ideally, an op amp has infinite input impedance (Zi), zero output impedance (Zo) and an open loop voltage gain (Av) of infinity. Obviously, practical op amps do not meet these specifications, but they do come closer than most other types of amplifiers. The gain of an op amp is the function of the input resistor and the feedback resistor. Gain is calculated by dividing the input resistor R1 value into the feedback resistor Rf. In figure E7-4 if the input resistor,R1, is 10,000 ohms and the feedback resistor ,Rf, 1s 1,000,000 ohms the gain would be 1,000,0000 / 10,000 or a gain of 100. The output is inverted in this configuration when the signal is feed into the – pin of the op amp. This is the most commonly used configuration. The op amp can be configured in a non inverting mode so the out put signal is the same polarity as the input signal Figure E7-4 The Ideal/perfect operational amplifier has Infinite gain, infinite frequency response , infinite input impedance and very low output impedance. E7G01 What primarily determines the gain and frequency characteristics of an op-amp RC active filter? The values of capacitors and resistors external to the op-amp E7G02 What is the effect of ringing in a filter? Undesired oscillations added to the desired signal E7G03 Which of the following is an advantage of using an op-amp instead of LC elements in an audio filter? Op-amps exhibit gain rather than insertion loss E7G04 Which of the following is a type of capacitor best suited for use in high-stability op-amp RC active filter circuits? Polystyrene E7G05 How can unwanted ringing and audio instability be prevented in a multi-section op-amp RC audio filter circuit? Restrict both gain and Q E7G06 Which of the following is the most appropriate use of an op-amp active filter? As an audio filter in a receiver E7G07 What magnitude of voltage gain can be expected from the circuit in Figure E7-4 when R1 is 10 ohms and RF is 470 ohms? 47 Rev 2.00 Page 81 AD7FO’s 2012-2016 Extra Class Syllabus E7G08 How does the gain of an ideal operational amplifier vary with frequency? It does not vary with frequency E7G09 What will be the output voltage of the circuit shown in Figure E7-4 if R1 is 1000 ohms, RF is 10,000 ohms, and 0.23 volts dc is applied to the input? -2.3 volts Gain = RF/ R1 or Gain = 10,000/1000 or Gain = 10 Output = input x Gain = .23 x 10 or - 2.3 volts. (Note the output is negative because it is an inverting amplifier) E7G10 What absolute voltage gain can be expected from the circuit in Figure E7-4 when R1 is 1800 ohms and RF is 68 kilohms? 38 Gain = RF/ R1 or Gain = 68,000/1,800 or Gain = 37.778 E7G11 What absolute voltage gain can be expected from the circuit in Figure E7-4 when R1 is 3300 ohms and RF is 47 kilohms? 14 Gain = RF/ R1 or Gain = 47,000/3,300 or Gain = 14.242 E7G12 What is an integrated circuit operational amplifier? A high-gain, direct-coupled differential amplifier with very high input and very low output impedance E7G13 What is meant by the term op-amp input-offset voltage? The differential input voltage needed to bring the open-loop output voltage to zero E7G14 What is the typical input impedance of an integrated circuit op-amp? Very high E7G15 What is the typical output impedance of an integrated circuit op-amp? Very low E7H Oscillators and signal sources: types of oscillators; synthesizers and phase-locked loops; direct digital synthesizers E7H01 What are three oscillator circuits used in Amateur Radio equipment? Colpitts, Hartley and Pierce E7H02 What condition must exist for a circuit to oscillate? It must have positive feedback with a gain greater than 1 Rev 2.00 Page 82 AD7FO’s 2012-2016 Extra Class Syllabus E7H03 How is positive feedback supplied in a Hartley oscillator? Through a tapped coil Remember Hartley uses a tapped coil for feedback. Henry is the measure of inductance of the coil in a Hartley oscillator. E7H04 How is positive feedback supplied in a Colpitts oscillator? Through a capacitive divider Remember C for Colpitts and capacitive divider E7H05 How is positive feedback supplied in a Pierce oscillator? Through a quartz crystal E7H06 Which of the following oscillator circuits are commonly used in VFOs? Colpitts and Hartley E7H07 What is a magnetron oscillator? A UHF or microwave oscillator consisting of a diode vacuum tube with a specially shaped anode, surrounded by an external magnet E7H08 What is a Gunn diode oscillator? An oscillator based on the negative resistance properties of properly-doped semiconductors Rev 2.00 Page 83 AD7FO’s 2012-2016 Extra Class Syllabus E7H09 What type of frequency synthesizer circuit uses a phase accumulator, lookup table, digital to analog converter and a low-pass anti-alias filter? A direct digital synthesizer Direct digital syntheses is a method of producing an analog waveform, usually a sine wave, by generating a time varying signal in digital form and then performing a digital-to-analog conversion. Because operations in a DDS are primarily digital it can offer fast switching between output frequencies, fine frequency resolution and operation over a broad spectrum of frequencies.. E7H10 What information is contained in the lookup table of a direct digital frequency synthesizer? The amplitude values that represent a sine-wave output E7H11 What are the major spectral impurity components of direct digital synthesizers? Spurious signals at discrete frequencies E7H12 Which of the following is a principal component of a direct digital synthesizer (DDS)? Phase accumulator E7H13 What is the capture range of a phase-locked loop circuit? The frequency range over which the circuit can lock E7H14 What is a phase-locked loop circuit? An electronic servo loop consisting of a phase detector, a low-pass filter, a voltage-controlled oscillator, and a stable reference oscillator E7H15 Which of these functions can be performed by a phase-locked loop? Frequency synthesis, FM demodulation E7H16 Why is the short-term stability of the reference oscillator important in the design of a phase locked loop (PLL) frequency synthesizer? Any phase variations in the reference oscillator signal will produce phase noise in the synthesizer output E7H17 Why is a phase-locked loop often used as part of a variable frequency synthesizer for receivers and transmitters? Rev 2.00 Page 84 AD7FO’s 2012-2016 Extra Class Syllabus It makes it possible for a VFO to have the same degree of frequency stability as a crystal oscillator E7H18 What are the major spectral impurity components of phase-locked loop synthesizers? Phase noise Rev 2.00 Page 85 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E8 - SIGNALS AND EMISSIONS [4 Exam Questions - 4 Groups] E8A AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; pulse and digital signal waveforms E8A01 What type of wave is made up of a sine wave plus all of its odd harmonics? A square wave E8A02 What type of wave has a rise time significantly faster than its fall time (or vice versa)? A sawtooth wave E8A03 What type of wave is made up of sine waves of a given fundamental frequency plus all its harmonics? A sawtooth wave E8A04 What is equivalent to the root-mean-square value of an AC voltage? The DC voltage causing the same amount of heating in a resistor as the corresponding RMS AC voltage RMS=.707 peak E8A05 What would be the most accurate way of measuring the RMS voltage of a complex waveform? By measuring the heating effect in a known resistor In precision measuring instruments a filament is heated with a current from an AC circuit and its temperature is measured by the voltage generated in a thermocouple attached to it. Then a DC current is applied to generate the same thermocouple voltage output. This dc current is then equal to the AC RMS current. Rev 2.00 Page 86 AD7FO’s 2012-2016 Extra Class Syllabus E8A06 What is the approximate ratio of PEP-to-average power in a typical single-sideband phone signal? 2.5 to 1 E8A07 What determines the PEP-to-average power ratio of a single-sideband phone signal? The characteristics of the modulating signal E8A08 What is the period of a wave? The time required to complete one cycle E8A09 What type of waveform is produced by human speech? Irregular This is because human speech is complex and contains many frequencies. E8A10 Which of the following is a distinguishing characteristic of a pulse waveform? Narrow bursts of energy separated by periods of no signal E8A11 What is one use for a pulse modulated signal? Digital data transmission E8A12 What type of information can be conveyed using digital waveforms? Human Speech Video Signals Data E8A13 What is an advantage of using digital signals instead of analog signals to convey the same information? Digital signals can be regenerated multiple times without error E8A14 Which of these methods is commonly used to convert analog signals to digital signals? Sequential sampling Rev 2.00 Page 87 AD7FO’s 2012-2016 Extra Class Syllabus E8A15 What would the waveform of a stream of digital data bits look like on a conventional oscilloscope? A series of pulses with varying patterns E8B Modulation and demodulation: modulation methods; modulation index and deviation ratio; pulse modulation; frequency and time division multiplexing E8B01 What is the term for the ratio between the frequency deviation of an RF carrier wave, and the modulating frequency of its corresponding FM-phone signal? Modulation index E8B02 How does the modulation index of a phase-modulated emission vary with RF carrier frequency (the modulated frequency)? It does not depend on the RF carrier frequency Modulation index = Deviation / Modulation frequency E8B03 What is the modulation index of an FM-phone signal having a maximum frequency deviation of 3000 Hz either side of the carrier frequency, when the modulating frequency is 1000 Hz? 3 (three) Modulation index = Deviation / Modulation frequency or 3000/1000 or 3.0 E8B04 What is the modulation index of an FM-phone signal having a maximum carrier deviation of plus or minus 6 kHz when modulated with a 2-kHz modulating frequency? 3 (three) Modulation index = Deviation / Modulation frequency or 6000/2000 or 3.0 E8B05 What is the deviation ratio of an FM-phone signal having a maximum frequency swing of plus-or-minus 5 kHz when the maximum modulation frequency is 3 kHz? 1.67 Deviation Ratio = Max Deviation / Max Modulation frequency or 5000/3000 or 1.666 Rev 2.00 Page 88 AD7FO’s 2012-2016 Extra Class Syllabus E8B06 What is the deviation ratio of an FM-phone signal having a maximum frequency swing of plus or minus 7.5 kHz when the maximum modulation frequency is 3.5 kHz? 2.14 Deviation Ratio = Max Deviation / Max Modulation frequency or 7500/3500 or 2.142 E8B07 When using a pulse-width modulation system, why is the transmitter's peak power greater than its average power? The signal duty cycle is less than 100% E8B08 What parameter does the modulating signal vary in a pulse-position modulation system? The time at which each pulse occurs E8B09 What is meant by deviation ratio? The ratio of the maximum carrier frequency deviation to the highest audio modulating frequency Deviation Ratio = maximum carrier deviation / highest modulating frequency . E8B10 Which of these methods can be used to combine several separate analog information streams into a single analog radio frequency signal? Frequency division multiplexing E8B11 Which of the following describes frequency division multiplexing? Two or more information streams are merged into a "baseband", which then modulates the transmitter E8B12 What is digital time division multiplexing? Two or more signals are arranged to share discrete time slots of a data transmission E8C Digital signals: digital communications modes; CW; information rate vs. bandwidth; spreadspectrum communications; modulation methods E8C01 Which one of the following digital codes consists of elements having unequal length? Morse code Rev 2.00 Page 89 AD7FO’s 2012-2016 Extra Class Syllabus E8C02 What are some of the differences between the Baudot digital code and ASCII? Baudot uses five data bits per character, ASCII uses seven or eight; Baudot uses two characters as shift codes, ASCII has no shift code E8C03 What is one advantage of using the ASCII code for data communications? It is possible to transmit both upper and lower case text E8C04 What technique is used to minimize the bandwidth requirements of a PSK31 signal? Use of sinusoidal data pulses In PSK31 (1's) are represented by a tone with no phase shift compared to the previous bit and (0's) are tone with a 180 degree phase shift relative to the phase of the previous bit. The phase shift occurs during the zero level modulation to minimize bandwidth. When the modulation level returns, the positions of the sine wave top and bottom are reversed from the previous bit. Thus the phase changes by 180 degrees while the frequency remains constant. E8C05 What is the necessary bandwidth of a 13-WPM international Morse code transmission? Approximately 52 Hz Required bandwidth = 4 times the character rate or 4 x13 = 52 E8C06 What is the necessary bandwidth of a 170-hertz shift, 300-baud ASCII transmission? 0.5 kHz E8C07 What is the necessary bandwidth of a 4800-Hz frequency shift, 9600-baud ASCII FM transmission? 15.36 kHz E8C08 What term describes a wide-bandwidth communications system in which the transmitted carrier frequency varies according to some predetermined sequence? Spread-spectrum communication E8C09 Which of these techniques causes a digital signal to appear as wide-band noise to a conventional receiver? Spread-spectrum E8C10 What spread-spectrum communications technique alters the center frequency of a conventional carrier many times per second in accordance with a pseudo-random list of channels? Frequency hopping E8C11 What spread-spectrum communications technique uses a high speed binary bit stream to shift the phase of an RF carrier? Rev 2.00 Page 90 AD7FO’s 2012-2016 Extra Class Syllabus Direct sequence E8C12 What is the advantage of including a parity bit with an ASCII character stream? Some types of errors can be detected E8C13 What is one advantage of using JT-65 coding? The ability to decode signals which have a very low signal to noise ratio JT65 is a digital protocol intended for Amateur Radio communication with extremely weak signals. It was designed to optimize Earth-Moon-Earth (EME) contacts on the VHF bands, and conforms efficiently to the established standards and procedures for such QSOs. E8D Waveforms: measurement, peak-to-peak, RMS, average; Electromagnetic Waves: definition, characteristics, polarization E8D01 Which of the following is the easiest voltage amplitude parameter to measure when viewing a pure sine wave signal on an analog oscilloscope? Peak-to-peak voltage E8D02 What is the relationship between the peak-to-peak voltage and the peak voltage amplitude of a symmetrical waveform? 2:1 The peak to peak includes both the positive and negative excursions of the sine wave, therefore it is twice the value of only the peak voltage. E8D03 What input-amplitude parameter is valuable in evaluating the signal-handling capability of a Class A amplifier? Peak voltage E8D04 What is the PEP output of a transmitter that develops a peak voltage of 30 volts into a 50-ohm load? 9 watts Step 1 - RMS= .707 x Peak or RMS = .707 x 30 or RMS = 21.21 Volts Step 2 – Power = (RMS)^2 / Resistance or P = (21.21)^2 / 50 or P = 449.86 / 50 or P = 8.997 Watts E8D05 If an RMS-reading AC voltmeter reads 65 volts on a sinusoidal waveform, what is the peak-to-peak voltage? 184 volts Peak to Peak = 2(RMS x 1.414) or PP = 2(65 x 1.414) or PP = 2 x 91.91 or PP 183.82 Volts Rev 2.00 Page 91 AD7FO’s 2012-2016 Extra Class Syllabus E8D06 What is the advantage of using a peak-reading wattmeter to monitor the output of a SSB phone transmitter? It gives a more accurate display of the PEP output when modulation is present E8D07 What is an electromagnetic wave? A wave consisting of an electric field and a magnetic field oscillating at right angles to each other E8D08 Which of the following best describes electromagnetic waves traveling in free space? Changing electric and magnetic fields propagate the energy E8D09 What is meant by circularly polarized electromagnetic waves? Waves with a rotating electric field E8D10 What type of meter should be used to monitor the output signal of a voice-modulated single-sideband transmitter to ensure you do not exceed the maximum allowable power? A peak-reading wattmeter E8D11 What is the average power dissipated by a 50-ohm resistive load during one complete RF cycle having a peak voltage of 35 volts? 12.2 watts Step 1 - RMS= .707 x Peak or RMS = .707 x 35 or RMS = 24.74 Volts Step 2 – Power = (RMS)^2 / Resistance or P = (24.74)^2 / 50 or P = 612.31 / 50 or P = 12.24 Watts E8D12 What is the peak voltage of a sinusoidal waveform if an RMS-reading voltmeter reads 34 volts? 48 volts Peak = 1.414 x RMS or Peak = 1.414 x 34 or peak = 48.07 volts E8D13 Which of the following is a typical value for the peak voltage at a standard U.S. household electrical outlet? 170 volts Peak = 1.414 x RMS or Peak = 1.414 x 120 or peak = 169.68 volts Rev 2.00 Page 92 AD7FO’s 2012-2016 Extra Class Syllabus 8D14 Which of the following is a typical value for the peak-to-peak voltage at a standard U.S. household electrical outlet? 340 volts Peak to Peak= 2 (1.414 x RMS) or PP = 2 (1.414 x 120) or PP = 2 x 169.68 or PP = 339.36 volts E8D15 Which of the following is a typical value for the RMS voltage at a standard U.S. household electrical power outlet? 120V AC E8D16 What is the RMS value of a 340-volt peak-to-peak pure sine wave? 120V AC RMS= (peak to Peak/2) / 1.414 or RMS= (340/2) / 1.414 or RMS= 170 / 1.414 or RMS = 120.22 volts Rev 2.00 Page 93 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E9 - ANTENNAS AND TRANSMISSION LINES [8 Exam Questions - 8 Groups] E9A Isotropic and gain antennas: definitions; uses; radiation patterns; Basic antenna parameters: radiation resistance and reactance, gain, beamwidth, efficiency E9A01 Which of the following describes an isotropic antenna? A theoretical antenna used as a reference for antenna gain E9A02 How much gain does a 1/2-wavelength dipole in free space have compared to an isotropic antenna? 2.15 dB Actually 2.14 dB gain, the test question answer is rounded to 2.15 dB E9A03 Which of the following antennas has no (zero) gain in any direction? Isotropic antenna E9A04 Why would one need to know the feed point impedance of an antenna? To match impedances in order to minimize standing wave ratio on the transmission line E9A05 Which of the following factors may affect the feed point impedance of an antenna? Antenna height, conductor length/diameter ratio and location of nearby conductive objects E9A06 What is included in the total resistance of an antenna system? Radiation resistance plus ohmic resistance E9A07 What is a folded dipole antenna? A dipole constructed from one wavelength of wire forming a very thin loop E9A08 What is meant by antenna gain? The ratio relating the radiated signal strength of an antenna in the direction of maximum radiation to that of a reference antenna Gain is generally expressed in dB relative to either an Isotropic source or a dipole. Rev 2.00 Page 94 AD7FO’s 2012-2016 Extra Class Syllabus E9A09 What is meant by antenna bandwidth? The frequency range over which an antenna satisfies a performance requirement Performance examples would be – Gain - SWR or impedance - Beam width – etc. E9A10 How is antenna efficiency calculated? (radiation resistance / total resistance) x 100% Can also be calculated by the equation: Efficiency = (Radiated Power / Input power x 100% E9A11 Which of the following choices is a way to improve the efficiency of a ground-mounted quarter-wave vertical antenna? Install a good radial system E9A12 Which of the following factors determines ground losses for a ground-mounted vertical antenna operating in the 3-30 MHz range? Soil conductivity E9A13 How much gain does an antenna have compared to a 1/2-wavelength dipole when it has 6 dB gain over an isotropic antenna? 3.85 dB The gain over isotropic source for an antenna with a 3.85 dB gain over a dipole antenna would be an additional 2.14 dB of gain. Remember dipole gain over an isotropic source is 2.14 dB or 3.85 dB +2.14dB or 5.99dB E9A14 How much gain does an antenna have compared to a 1/2-wavelength dipole when it has 12 dB gain over an isotropic antenna? 9.85 dB Remember that a dipole has 2.14 dB of gain as referenced to an isotropic antenna. 12 dB -2.14 dB or gain =9.86dB E9A15 What is meant by the radiation resistance of an antenna? The value of a resistance that would dissipate the same amount of power as that radiated from an antenna E9B Antenna patterns: E and H plane patterns; gain as a function of pattern; antenna design (computer modeling of antennas); Yagi antennas Figure E9-1 120 150 -3 -6 -12 60 Free-Space Pattern 30 -24 180 -150 0 -30 -60 -120 E9B01 In the antenna radiation pattern shown in Figure E9-1, what is the 3-dB beamwidth? 50 degrees E9B02 In the antenna radiation pattern shown in Figure E9-1, what is the front-to-back ratio? Rev 2.00 Page 95 AD7FO’s 2012-2016 Extra Class Syllabus 18 dB E9B03 In the antenna radiation pattern shown in Figure E9-1, what is the front-to-side ratio? 14 dB E9B04 What may occur when a directional antenna is operated at different frequencies within the band for which it was designed? The gain may change depending on frequency E9B05 What usually occurs if a Yagi antenna is designed solely for maximum forward gain? The front-to-back ratio decreases The front to back ratio is important in circumstances where interference or coverage in the reverse direction needs to be minimised. Unfortunately the conditions within the antenna mean that optimisation has to be undertaken for either front to back ratio, or maximum forward gain. Conditions for both features do not coincide, but the front to back ratio can normally be maximised for a small degradation of the forward gain. E9B06 If the boom of a Yagi antenna is lengthened and the elements are properly retuned, what usually occurs? The gain increases E9B07 How does the total amount of radiation emitted by a directional gain antenna compare with the total amount of radiation emitted from an isotropic antenna, assuming each is driven by the same amount of power? They are the same Remember the key word is total power. In an isotropic antenna power is equally radiated in all directions. In a gain antenna the power is focused in one direction so in that direction it is stronger but in other directions it is weaker. Total power is the sum of all power in all directions assuming both antennas are 100% efficient. E9B08 How can the approximate beamwidth in a given plane of a directional antenna be determined? Note the two points where the signal strength of the antenna is 3 dB less than maximum and compute the angular difference E9B09 What type of computer program technique is commonly used for modeling antennas? Method of Moments Rev 2.00 Page 96 AD7FO’s 2012-2016 Extra Class Syllabus E9B10 What is the principle of a Method of Moments analysis? A wire is modeled as a series of segments, each having a uniform value of current E9B11 What is a disadvantage of decreasing the number of wire segments in an antenna model below the guideline of 10 segments per half-wavelength? The computed feed point impedance may be incorrect E9B12 What is the far-field of an antenna? The region where the shape of the antenna pattern is independent of distance E9B13 What does the abbreviation NEC stand for when applied to antenna modeling programs? Numerical Electromagnetics Code E9B14 What type of information can be obtained by submitting the details of a proposed new antenna to a modeling program? A. SWR vs. frequency charts B. Polar plots of the far-field elevation and azimuth patterns C. Antenna gain D. All of these choices are correct E9C Wire and phased vertical antennas: beverage antennas; rhombic antennas; elevation above real ground; ground effects as related to polarization; take-off angles E9C01 What is the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase? A figure-8 oriented along the axis of the array E9C02 What is the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/4-wavelength apart and fed 90 degrees out of phase? A cardioid E9C03 What is the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed in phase? A Figure-8 broadside to the axis of the array Two 1/4 wavelength verticals 1/2 wavelength apart, fed in phase E9C04 Rev 2.00 Page 97 AD7FO’s 2012-2016 Extra Class Syllabus Which of the following describes a basic unterminated rhombic antenna? Bidirectional; four-sides, each side one or more wavelengths long; open at the end opposite the transmission line connection E9C05 What are the disadvantages of a terminated rhombic antenna for the HF bands? The antenna requires a large physical area and 4 separate supports E9C06 What is the effect of a terminating resistor on a rhombic antenna? It changes the radiation pattern from bidirectional to unidirectional polarization Figure E9-2 90 120 Over Real Ground 60 150 180 30 -40 -30 -20 -10 0 E9C07 What type of antenna pattern over real ground is shown in Figure E9-2? Elevation E9C08 What is the elevation angle of peak response in the antenna radiation pattern shown in Figure E9-2? 7.5 degrees E9C09 What is the front-to-back ratio of the radiation pattern shown in Figure E9-2? 28 dB E9C10 How many elevation lobes appear in the forward direction of the antenna radiation pattern shown in Figure E9-2? 4 (four) E9C11 How is the far-field elevation pattern of a vertically polarized antenna affected by being mounted over seawater versus rocky ground? The low-angle radiation increases Rev 2.00 Page 98 AD7FO’s 2012-2016 Extra Class Syllabus E9C12 When constructing a Beverage antenna, which of the following factors should be included in the design to achieve good performance at the desired frequency? It should be one or more wavelengths long E9C13 What is the main effect of placing a vertical antenna over an imperfect ground? It reduces low-angle radiation E9D Directional antennas: gain; satellite antennas; antenna beamwidth; stacking antennas; antenna efficiency; traps; folded dipoles; shortened and mobile antennas; grounding E9D01 How does the gain of an ideal parabolic dish antenna change when the operating frequency is doubled? Gain increases by 6 dB E9D02 How can linearly polarized Yagi antennas be used to produce circular polarization? Arrange two Yagis perpendicular to each other with the driven elements at the same point on the boom and fed 90 degrees out of phase E9D03 How does the beamwidth of an antenna vary as the gain is increased? It decreases E9D04 Why is it desirable for a ground-mounted satellite communications antenna system to be able to move in both azimuth and elevation? In order to track the satellite as it orbits the Earth E9D05 Where should a high-Q loading coil be placed to minimize losses in a shortened vertical antenna? Near the center of the vertical radiator Rev 2.00 Page 99 AD7FO’s 2012-2016 Extra Class Syllabus E9D06 Why should an HF mobile antenna loading coil have a high ratio of reactance to resistance? To minimize losses E9D07 What is a disadvantage of using a multiband trapped antenna? It might radiate harmonics E9D08 What happens to the bandwidth of an antenna as it is shortened through the use of loading coils? It is decreased E9D09 What is an advantage of using top loading in a shortened HF vertical antenna? Improved radiation efficiency E9D10 What is the approximate feed point impedance at the center of a two-wire folded dipole antenna? 300 ohms E9D11 What is the function of a loading coil as used with an HF mobile antenna? To cancel capacitive reactance E9D12 What is one advantage of using a trapped antenna? It may be used for multiband operation Rev 2.00 Page 100 AD7FO’s 2012-2016 Extra Class Syllabus E9D13 What happens to feed point impedance at the base of a fixed-length HF mobile antenna as the frequency of operation is lowered? The radiation resistance decreases and the capacitive reactance increases E9D14 Which of the following types of conductor would be best for minimizing losses in a station's RF ground system? A wide flat copper strap E9D15 Which of the following would provide the best RF ground for your station? An electrically-short connection to 3 or 4 interconnected ground rods driven into the Earth E9E Matching: matching antennas to feed lines; power dividers E9E01 What system matches a high-impedance transmission line to a lower impedance antenna by connecting the line to the driven element in two places spaced a fraction of a wavelength each side of element center? The delta matching system E9E02 What is the name of an antenna matching system that matches an unbalanced feed line to an antenna by feeding the driven element both at the center of the element and at a fraction of a wavelength to one side of center? The gamma match Rev 2.00 Page 101 AD7FO’s 2012-2016 Extra Class Syllabus E9E03 What is the name of the matching system that uses a section of transmission line connected in parallel with the feed line at or near the feed point? The stub match E9E04 What is the purpose of the series capacitor in a gamma-type antenna matching network? To cancel the inductive reactance of the matching network E9E05 How must the driven element in a 3-element Yagi be tuned to use a hairpin matching system? The driven element reactance must be capacitive E9E06 What is the equivalent lumped-constant network for a hairpin matching system on a 3-element Yagi? L network E9E07 What term best describes the interactions at the load end of a mismatched transmission line? Reflection coefficient E9E08 Which of the following measurements is characteristic of a mismatched transmission line? An SWR greater than 1:1 Rev 2.00 Page 102 AD7FO’s 2012-2016 Extra Class Syllabus E9E09 Which of these matching systems is an effective method of connecting a 50-ohm coaxial cable feed line to a grounded tower so it can be used as a vertical antenna? Gamma match E9E10 Which of these choices is an effective way to match an antenna with a 100-ohm feed point impedance to a 50-ohm coaxial cable feed line? Insert a 1/4-wavelength piece of 75-ohm coaxial cable transmission line in series between the antenna terminals and the 50-ohm feed cable E9E11 What is an effective way of matching a feed line to a VHF or UHF antenna when the impedances of both the antenna and feed line are unknown? Use the universal stub matching technique E9E12 What is the primary purpose of a phasing line when used with an antenna having multiple driven elements? It ensures that each driven element operates in concert with the others to create the desired antenna pattern E9E13 What is the purpose of a Wilkinson divider? It divides power equally among multiple loads while preventing changes in one load from disturbing power flow to the others Rev 2.00 Page 103 AD7FO’s 2012-2016 Extra Class Syllabus E9F Transmission lines: characteristics of open and shorted feed lines; 1/8 wavelength; 1/4 wavelength; 1/2 wavelength; feed lines: coax versus open-wire; velocity factor; electrical length; coaxial cable dielectrics; velocity factor E9F01 What is the velocity factor of a transmission line? The velocity of the wave in the transmission line divided by the velocity of light in a vacuum E9F02 Which of the following determines the velocity factor of a transmission line? Dielectric materials used in the line Velocity Factor = Velocity of wave in Transmission line / Velocity of light E9F03 Why is the physical length of a coaxial cable transmission line shorter than its electrical length? Electrical signals move more slowly in a coaxial cable than in air E9F04 What is the typical velocity factor for a coaxial cable with solid polyethylene dielectric? 0.66 E9F05 What is the approximate physical length of a solid polyethylene dielectric coaxial transmission line that is electrically onequarter wavelength long at 14.1 MHz? (Assuming a velocity factor of 0.66) 3.5 meters ¼ Wavelength (in Transmission line) = (300/F(MHz)) / 4 x Velocity Factor ¼ Wavelength (in Transmission line) =(300/14.1 x .66) / 4 or 14.04/4 or 3.51 meters E9F06 What is the approximate physical length of an air-insulated, parallel conductor transmission line that is electrically one-half wavelength long at 14.10 MHz? (Assuming a velocity factor of 0.95) 10 meters ½ Wavelength (in Transmission line) = (300/F(MHz))/2 x Velocity Factor ½ Wavelength (in Transmission line) = (300/14.1 x .95)/2 or 20.21/2 or 10.10 meters E9F07 How does ladder line compare to small-diameter coaxial cable such as RG-58 at 50 MHz? Lower loss E9F08 What is the term for the ratio of the actual speed at which a signal travels through a transmission line to the speed of light in a vacuum? Velocity factor Rev 2.00 Page 104 AD7FO’s 2012-2016 Extra Class Syllabus E9F09 What is the approximate physical length of a solid polyethylene dielectric coaxial transmission line that is electrically onequarter wavelength long at 7.2 MHz? (Assuming a velocity factor of 0.66) 6.9 meters ¼ Wavelength(in Transmission line) = (300/F(MHz))/4 x Velocity Factor ¼ Wavelength(in Transmission line) =(300/7.2 x..66)/4 or 27.50/4 or 6.87 meters E9F10 What impedance does a 1/8-wavelength transmission line present to a generator when the line is shorted at the far end? An inductive reactance Stub Length E9F11 What impedance does a 1/8-wavelength transmission line present to a generator when the line is open at the far end? A capacitive reactance E9F12 What impedance does a 1/4-wavelength transmission line present to a generator when the line is open at the far end? Very low impedance E9F13 What impedance does a 1/4-wavelength transmission line present to a generator when the line is shorted at the far end? Very high impedance E9F14 What impedance does a 1/2-wavelength transmission line present to a generator when the line is shorted at the far end? Very low impedance E9F15 What impedance does a 1/2-wavelength transmission line present to a generator when the line is open at the far end? Very high impedance E9F16 Which of the following is a significant difference between foam-dielectric coaxial cable and solid-dielectric cable, assuming all other parameters are the same? A. Reduced safe operating voltage limits B. Reduced losses per unit of length C. Higher velocity factor D. All of these choices are correct E9G The Smith chart For a tutorial on smith charts go to http://www.maxim-ic.com/app-notes/index.mvp/id/742 E9G01 Which of the following can be calculated using a Smith chart? Impedance along transmission lines Rev 2.00 Page 105 AD7FO’s 2012-2016 Extra Class Syllabus E9G02 What type of coordinate system is used in a Smith chart? Resistance circles and reactance arcs E9G03 Which of the following is often determined using a Smith chart? Impedance and SWR values in transmission lines E9G04 What are the two families of circles and arcs that make up a Smith chart? Resistance and reactance Figure E9-3 E9G05 What type of chart is shown in Figure E9-3? Smith chart E9G06 On the Smith chart shown in Figure E9-3, what is the name for the large outer circle on which the reactance arcs terminate? Reactance axis Rev 2.00 Page 106 AD7FO’s 2012-2016 Extra Class Syllabus E9G07 On the Smith chart shown in Figure E9-3, what is the only straight line shown? The resistance axis E9G08 What is the process of normalization with regard to a Smith chart? Reassigning impedance values with regard to the prime center E9G09 What third family of circles is often added to a Smith chart during the process of solving problems? Standing-wave ratio circles E9G10 What do the arcs on a Smith chart represent? Points with constant reactance E9G11 How are the wavelength scales on a Smith chart calibrated? In fractions of transmission line electrical wavelength E9H Effective radiated power; system gains and losses; radio direction finding antennas E9H01 What is the effective radiated power relative to a dipole of a repeater station with 150 watts transmitter power output, 2-dB feed line loss, 2.2-dB duplexer loss and 7-dBd antenna gain? 286 watts ERP = Power + gain(s) – Loss(es) ERP= 150 watts + (7 dB) – (2 dB + 2.2 dB) or 150 watts + 2.8 dB Gain/loss ratio = 10^(dB/10)or 10^(2.8/10) or 10^.28 or 1.905 ERP = 150 watts x 1.905(the overall db gain/loss ratio) or 285.8 watts E9H02 What is the effective radiated power relative to a dipole of a repeater station with 200 watts transmitter power output, 4-dB feed line loss, 3.2-dB duplexer loss, 0.8-dB circulator loss and 10-dBd antenna gain? 317 watts ERP = Power + gain(s) – Loss(es) ERP= 150 watts + (10 dB) – (4 dB + 3.2 dB +0.8 dB) or 150 watts + 2 dB Gain/loss ratio = 10^(dB/10)or 10^(2.0/10) or 10^.20 or 1.584 ERP = 200 watts x 1.584(the overall db gain/loss ratio) or 316.9 watts E9H03 What is the effective isotropic radiated power of a repeater station with 200 watts transmitter power output, 2-dB feed line loss, 2.8-dB duplexer loss, 1.2-dB circulator loss and 7-dBi antenna gain? 252 watts ERP = Power + gain(s) – Loss(es) ERP= 200 watts + (7 dB) – (2 dB + 2.8 dB +1.2 dB) or ERP = 200 watts + 1 dB Gain/loss ratio = 10^(dB/10) or 10^(1/10) or 10^.1 or 1.258 ERP = 200 watts x 1.258 (the overall db gain/loss ratio) or 251.7 watts E9H04 What term describes station output, including the transmitter, antenna and everything in between, when considering transmitter power and system gains and losses? Effective radiated power E9H05 What is the main drawback of a wire-loop antenna for direction finding? Rev 2.00 Page 107 AD7FO’s 2012-2016 Extra Class Syllabus It has a bidirectional pattern E9H06 What is the triangulation method of direction finding? Antenna headings from several different receiving locations are used to locate the signal source E9H07 Why is it advisable to use an RF attenuator on a receiver being used for direction finding? It prevents receiver overload which could make it difficult to determine peaks or nulls E9H08 What is the function of a sense antenna? It modifies the pattern of a DF antenna array to provide a null in one direction E9H09 Which of the following describes the construction of a receiving loop antenna? One or more turns of wire wound in the shape of a large open coil E9H10 How can the output voltage of a multi-turn receiving loop antenna be increased? By increasing either the number of wire turns in the loop or the area of the loop structure or both E9H11 What characteristic of a cardioid-pattern antenna is useful for direction finding? A very sharp single null E9H12 What is an advantage of using a shielded loop antenna for direction finding? It is electro-statically balanced against ground, giving better nulls Rev 2.00 Page 108 AD7FO’s 2012-2016 Extra Class Syllabus SUBELEMENT E0 – SAFETY - [1 exam question -– 1 group] E0A Safety: amateur radio safety practices; RF radiation hazards; hazardous materials E0A01 What, if any, are the differences between the radiation produced by radioactive materials and the electromagnetic energy radiated by an antenna? Radioactive materials emit ionizing radiation, while RF signals have less energy and can only cause heating E0A02 When evaluating RF exposure levels from your station at a neighbor’s home, what must you do? Make sure signals from your station are less than the uncontrolled MPE limits E0A03 Which of the following would be a practical way to estimate whether the RF fields produced by an amateur radio station are within permissible MPE limits? Use an antenna modeling program to calculate field strength at accessible locations E0A04 When evaluating a site with multiple transmitters operating at the same time, the operators and licensees of which transmitters are responsible for mitigating over-exposure situations? Each transmitter that produces 5% or more of its MPE exposure limit at accessible locations E0A05 What is one of the potential hazards of using microwaves in the amateur radio bands? The high gain antennas commonly used can result in high exposure levels For example a transmitter at 2.5 GHz with a power output of 100 watts and an antenna gain of 12 dB would be the equivalent of 800 watts in the direction the antenna is pointing. Your home microwave oven operates at about this frequency with a power output of around 600 watts. Would you stand in front of your microwave oven with the door open and operating? E0A06 Why are there separate electric (E) and magnetic (H) field MPE limits? A. The body reacts to electromagnetic radiation from both the E and H fields B. Ground reflections and scattering make the field impedance vary with location C. E field and H field radiation intensity peaks can occur at different locations D. All of these choices are correct E0A07 How may dangerous levels of carbon monoxide from an emergency generator be detected? Only with a carbon monoxide detector E0A08 What does SAR measure? The rate at which RF energy is absorbed by the body SAR is short for Specific Absorption Rate E0A09 Which insulating material commonly used as a thermal conductor for some types of electronic devices is extremely toxic if broken or crushed and the particles are accidentally inhaled? Beryllium Oxide E0A10 What material found in some electronic components such as high-voltage capacitors and transformers is considered toxic? Polychlorinated biphenyls (PCB’s) E0A11 Which of the following injuries can result from using high-power UHF or microwave transmitters? Localized heating of the body from RF exposure in excess of the MPE limits Rev 2.00 Page 109 AD7FO’s 2012-2016 Extra Class Syllabus Reference materials Rev 2.00 Page 110 AD7FO’s 2012-2016 Extra Class Syllabus International System of Units (SI)—Metric Units Prefix Symbol ————Multiplication Factor——— exe E 10+18 1,000,000 000,000,000,000 peta P 10+15 1,000 000,000,000,000 tera T 10+12 1,000,000,000,000 giga G 10+9 1,000,000,000 mega M 10+6 1,000,000 kilo k 10+3 1,000 hecto h 10+2 100 deca da 10+1 10 (unit) 10+0 1 deci d 10-1 0.1 centi c 10-2 0.01 milli m 10-3 0.001 micro μ 10-6 0.000001 nano n 10-9 0.000000001 pico p 10-12 0.000000000001 femto f 10-15 0.000000000000001 atto a 10-18 0.000000000000000001 Scientific Notation to component values Milli m= .001 or Micro µ = .000,001 or Nano n= .000,000,001 or Pico p= .000,000,000,001 or Fempto f= .000,000,000,000,001 or 1x 10^-3 1x 10^-6 1 x 10^-9 1 x 10^-12 1 x 10^-15 Ohms Law I=E/R R=E/I E=I * R (Amperes – Volts-Ohms) P=E * I P= E² /R I= P/E (amperes-volts-ohms-watts) Series connected Resistors R = R1 + R2 + R3 + Rx Parallel connected Resistors R= ___________________1__________ 1 1 1 ….._1__ R1 + R2 + R3 + Rx Series inductors Total Inductance = L1 + L2 + L3 + Lx Parallel inductors L= ___________________1__________ 1 1 1 ….._1__ L1 + L2 + L3 + Lx Capicators in parallel C = C1 + C2 + C3 + Rev 2.00 Cx Page 111 AD7FO’s 2012-2016 Extra Class Syllabus Capacitors in series C= ___________________1__________ 1 1 1 ….._1__ C1 + C2 + C3 + Cx Reactance Reactance is the equivalent AC resistance of a capacitor or inductor at a given frequency For an inductor, XL =2πFL XL =2πFL frequency is in Hertz and Inductance is in Henries. or Hertz or Micro-Henries and Megahertz Mili-Henries and Kilo- Example 20 mH inductor at 3.5 KHz XL =2πFL = 6.28 x .02 x 3,500 = 6.28x 70 = 439.8 Ω OR XL =2πFL = 6.28 x 20 x 3.5 = 6.28x 70 = 439.8 Ω OR XL =2πFL = 6.28 x 20,000 x .0035 = 6.28x 70 = 439.8 Ω For a capacitor Reactance (Xc) is equal to 1/ (2π FC) and Megahertz frequency is in Hertz and Capacitance is in Farads. or Microfarads Example 20 µF Capacitor at 3.5 KHz Xc =1/(2πFC) = 1/(6.28 x .000,020 x 3,500) = 1/(6.28x .07) = 2.27 Ω OR Xc =1/(2πFC) = 1/(6.28 x 20 x .0035) = 1/(6.28 x .7) = 1/.44 = 2.27 Ω RC Time Constant TC = C * R farads - ohms or microfarads – megohms Charge vs number of time constants Time Constant % Charge / Discharge 1 63.2 2 86.5 3 95 4 98.2 5 99.3 dB Calculations Power dB = 10 * LOG (P1/P2) P1 andP2 must be the same i.e.: µWatts. Miliwatts or Watts Voltage - dB = 20 * LOG (V1/V2) V1 and V2 must be the same i.e.: µvolts. Milivolts or Volts The following table will allow you to quickly estimate dB gain or loss. The one and two dB values are close enough to get you to the correct answer in the test. Gain (+) x 1.2 x 1.6 x2 x4 x 10 Rev 2.00 dB Loss (-) 1 2 3 6 10 80% 63% 50% 25% 10% Page 112 AD7FO’s 2012-2016 Extra Class Syllabus Noise Figure vs Sensitivity Noise figure is what the front end amplifier adds to the theoretical noise floor Theoretical noise floor is -174dBm in a 1HZ bandwidth. For a 500 HZ receiver bandwidth this would be: Noise Floor Noise Floor = -174 + 10*Log (500/1) dB or -174dBm +27dB or -147 dBm If in the Previous example our receiver has a noise figure of 8dB then the smallest signal you could possibly receive would need to be 8 dB larger. : Noise floor would be -147 dBm + 8 dB or -139 dBm or about .03µV Blocking dynamic range The blocking dynamic range of a receiver that has an 8 db noise figure and an IF bandwidth of 500 Hz and a -1 dB compression point of -20dBm is 119 db Theoretical noise floor for 500 Hz bandwidth is -147dBm Noise Floor = -174 dBm + (10 log (1/500) ))dB Noise floor = - 174 dBm +(10 log (.002))dB Noise floor = - 174 dBm +27dB Noise floor = - 147 dBm Add the +8 db Noise figure to the noise floor and get the actual noise floor of -139 dBm. Receiver Noise floor = theoretical noise floor plus noise figure Receiver Noise floor = -147dBm + 8dB = -139 dBm Subtracting the – 20 dBm compression point gives us a difference of 119dB which is the Blocking dynamic range. Blocking Dynamic range = Receiver Noise floor – 1 dBCompression point Blocking Dynamic range = -139 –( – 20 dB) = -119 dB Blocking Dynamic range is expressed as a positive number so the answer is 119 dB For a 2.8 KHz wide receiver the theoretical noise floor with a 5 dB noise figure would be -174dBm + 10 * LOG (2800/1) + 5 Or -174 + 34.5 + 5 or – 134.5 dB Rev 2.00 Page 113 AD7FO’s 2012-2016 Extra Class Syllabus Impedance of complex series circuits Impedance 100 Ohms XL Inductive reactance 100 ohms R Series circuit Impedance = √(resistance²+ reactance²) = √(10,000+10,000) =√20,000=141.4 Ohms Angle = arc tangent =Opposite/Adjacent or arc tangent =100/100 or Arc tangent (1.00) = 45 º The equation for calculating Impedance given resistance and inductive and/or capacitive reactance is: Impedance (Z) = √(R² +Reactance²) For a circuit with 53 Ohms of resistance and 25 ohms of reactance (either Inductive or capacitive) it would be: Z= √[(53)² +(15)²)] = √ 3034 = 55Ω For a circuit with 35 Ohms resistance, 38 Ohms Inductive reactance 50 Ohms Capacitive Reactance. The resistor value in this problem is 35 ohms and the reactance is 38 (inductance is +) + (- 50ohms) (capacitive reactance is -) or a total reactive value of -12 ohms (capacitive) Z = √[(35)² +(38-50)²] = √[(35)² +(12)²] = √1369 = 37 Ω Remember that Impedance is never less than the resistance in the circuit. Component Q The Q of a capacitor or inductor can be calculated from the following equations: Capacitor Q= Capacitive Reactance/ resistance Inductor Q= Inductive Reactance/ resistance The Q of a parallel RLC network with a 8.2 µH inductor, R of 1000 Ω with a resonant frequency of 7.125 MHz is 0.23: Q= R/Reactance = R/ (2π FL) = 220/ (6.28*3.625*42) = 220/956.6 = 0.230 The Q of a parallel RLC network with a 42 µH inductor, R of 220 Ω with a resonant frequency of 7.125 MHz is 2.72: Q= R/Reactance = R/ (2π FL) = 1000/ (6.28*7.125*8.2) = 1000/367.09 = 2.724 Rev 2.00 Page 114 AD7FO’s 2012-2016 Extra Class Syllabus Effective Radiated Power Lets take an example with the following characteristics: o Power output from radio = 50 watts o Feed line loss = - 4dB o Duplexer loss = -2 dB o Circulator loss = - 1dB o Antenna Gain =+ 4 dB First we calculate the overall ERP as follows: ERP=Transmitter Power Out = +((-4)+(-2)+(-=1)+(+4)) = 50 - 3 dB or 25 watts Resonant circuits § In any resonant circuit the X L is equal to the XC at resonance § In a series resonant circuit the impedance at the resonant frequency is zero § In a parallel resonant circuit the impedance at resonance is ∞ § In a parallel resonant circuit with perfect components once the circuit is energized it will continue to oscillate forever with the capacitor charging the inductor then the inductor charging the capacitor. Since our components are not perfect this will not happen. Series resonant circuits Series Resonant Circuits look like a short to the signal source (assuming ideal components) with the only limit on current being the resistance of the components and any external resistance added in series Series Resonant Frequency is determined by the following equation with Frequency in Hertz, Inductance in Henries and Capacity in farads. (or frequency in kHz, inductance in mH and capacity in µ Henries and µH) 1 FR = 2π√(LC) For a circuit with an inductance of 50 µH and 40 pF FR = 1/ (2π√(LC)) = 1/(6.28 √(.000050 x .000,000,000,040) = 3,558,812 Hz or FR = 1/ (2π√(LC)) = 1/(6.28 √(50 x . 000,040) = 3.559 kHz Parallel Resonant circuits Has high output voltage and looks like a high resistance (or in a perfect circuit an open circuit) to the signal source. Calculating resonant frequency for a parallel inductor and capacitor circuit: Resonant frequency = 1/ (2π √ (LC) ) Let’s calculate the resonant frequency for a circuit a circuit with a 10 µH inductor and 300 pf capacitor. Remember that this equation requires the inductance to be in Henries and capacitance in Farads, the resonant frequency answer will be in Hz. F = 1/ (2π √ (LC) ) = 1/ (2 π √ ((10 ↑-6) * (300 ↑-12)) = 1/ (2 π √(30↑-16)) F= 2,900,000 Hz or 2.9 MHz If you need to determine which L or C component is needed to resonate at a specific frequency, the following equations can be used: L= 1/((2 π F)² C) Rev 2.00 or C= 1/((2 π F)² L) Page 115 AD7FO’s 2012-2016 Extra Class Syllabus Calculating Component values for resonance At a specific frequency Capacity in Farads, Inductance in Henries, and Frequency in Hertz (or frequency in MHz, Inductance in µH and capacity in µF ): 1 1 C= L= (2πFR)² L (2πFR)² C Find the capacitor value for: A resonant frequency of F=3,600,000 Hz (3.6 MHz) A 20µH (.000,020 H) inductor: C= 1/(6.28 x 3,600,000)² x 000020 = 1/(.000516) x 20 = 1/ 10,23 = 97.7 ^-12F or 98 pF Or C = 1/(6.28 x 3.6)² x 20 = 1/(511.6 x 20) = 1/ 10.23 = 97.7 ^-6 µ F or 98 pF For 7.3 MHz and 19µH C = 1/(6.28 x 7.3)² x 19 = 25pF For 21 MHz and 3 µH C = 1/(6.28 x 21)² x 3 = 19.1 pF Finding an Inductor value For a resonant frequency of 10 MHz with a capacitor of 10 pF L = 1/(6.28 x 10)² x .000,010 = 1/(39.44 x .000,010 = 1/ .39.44 = 25µH A resonant frequency of 21 MHz with a capacitor of 7 pF L = 1/(6.28 x 21)² x .000,007 = 8.21µH A resonant frequency of 7.3 MHz with a capacitor of 25 pF L = 1/(6.28 x 7.3)² x .000,025 = 19µH Resonant Circuit Q Q for a resonant circuit is a function of the circuit resistance vs the reactance at a given frequency. For a series circuit Q = XL /R Example- a circuit with 1000 ohms of inductive reactance and 100 ohms of resistance would be Q = 1000 / 100 or 10 For a parallel circuit Q = Resistance /Reactance Example a circuit with 500 ohms of Inductive reactance and 100 Ohms And 10,000 ohms of parallel resistance would be Q = 10,000 / 500 or 20 The bandwidth of the resonant circuit The 3 dB bandwidth of a resonant circuit is equal to: Bandwidth = Resonant Frequency / Q A circuit resonant at 3.5 MHz with a Q of 50 would have a bandwidth of 3,500,000 / 50 or 70 kHz A circuit resonant at 25 MHz with a Q of 85 would have a bandwidth of 25,000,000 / 85 or 294 kHz A circuit resonant at 7.25 MHz with a Q of 180 would have a bandwidth of 7,250,000 / 180 or 40.3 kHz Rev 2.00 Page 116 AD7FO’s 2012-2016 Extra Class Syllabus Power Factor Power Factor is the Cosine of the impedance angle this a number between 1 and 0 and represents a ratio between the real and the apparent power in the circuit If you know the magnitude of the resistance and Reactance you can determine power factor and real power from their angle as a tangent function (Opposite over Adjacent sides of a right triangle), then determine the cosine function of that angle, this will be the circuit ‘ power factor’ Example 1 - For a circuit with resistance of 50 ohms and a reactance of 19 ohms, you would calculate the power factor as follows: o Find the tangent function -tangent = opposite/ adjacent = 10 / 50 = .2 o Using a calculator find the angle whose tangent is .2 = 11° o Using a calculator find the cosine of 11° = .982 Example 2 - For a circuit with resistance of 30 ohms and a reactance of 17 ohms, you would calculate the power factor as follows: o Find the tangent function -tangent = opposite/ adjacent = 17 / 30 = .567 o Using a calculator find the angle whose tangent is .567 = 29.5° o Using a calculator find the cosine of 29.5° = .87 If you know the real and the apparent power you can calculate the power factor directly using the equation: Power Factor = P real / P apparent For a circuit with an apparent power of 120VA and a real power of 100 watts the power factor would be 100/120 or .833. For a circuit with an apparent power of 400VA and a power factor of .2 the real power would be 400 x .2 or 80 Watts Operational Amplifiers Gain = R(feedback) /R(input) If the feedback resistor was 100,000 Ω and the input resistor was 1,000 Ω the gain would be 100,000/1,000 or 100. Since the input impedance is very high there is no current flowing through Rinput, and the voltage applied is accurately amplified. Rev 2.00 Page 117 AD7FO’s 2012-2016 Extra Class Syllabus AC Voltage Calculations The RMS (Root Mean Square) value for a sine wave is the value of an equivalent DC voltage required to generate the same amount of power or heat in a resistive load For a pure sine wave the equivalent RMS value is .707 times the peak value. Conversely the peak voltage can be calculated as 1.414 times the RMS Value. The peak voltage for standard 120V RMS AC line voltage is Peak Voltage = 1.414 x 120V or ~170 volts peak. The peak to peak would be two times the peak voltage Voltage Peak to peak = 2 x 170 or 340 Volts pp An AC voltage that reads 65 volts on an RMS meter will have a peak to peak voltage of Peak to Peak = 65 x 1.414 x 2 or ~184 Volts. The average power dissipated by a 50 ohm resistor during one cycle of voltage with a peak voltage of 35 volts is 12.2 Watts. P(avge)= E² (avge) / R = (.707 x 35)² / 50 = 12.2 Watts FM Modulation Modulation Index M index = Deviation /Modulating Frequency The Modulation Index for a FM phone signal with 3 KHz deviation and a 1 KHz tone would be: M Index = 3,000/1,000 = 3 From the above equation you can see that Modulation index is independent of the carrier frequency Deviation Ratio Deviation Ratio = Maximum Deviation / Maximum modulating frequency For a FM phone transmission with a ± 5 KHz deviation and a 3 KHz maximum modulating tone the deviation ration would be: Deviation ratio= 5,000/3,000 = 1.67 Deviation ratio describes a maximum event (max deviations and max audio frequency, while modulation index describes an instantaneous set of conditions Transmitter Power Measurements The PEP power output for a transmitter with an observed 30 volt peak envelope voltage (as seen on an oscilloscope) would be 9 watts. To determent the PEP power we take the peak voltage and multiply it by >707 to get the Peak RMS voltage then using the Peak RMS voltage we calculate power using the equation P(watts) = V(RMS)² / R (load) PEP (watts) = [ V(peak) x .707 ]² / Load Resistance PEP (watts) = [ V(peak) x .707 ]² / 50 = (21.2)²/ 50 = 449 / 50 = 9 Amplifier efficiency Amplifier efficiency is the ratio of power divided by power input times 100%. Efficiency = P(out) / P(input) x 100 A typical 1500 Watt PEP class B amplifier will require 2500 watts of DC input power (assume 60% efficiency). A typical class A amplifier will be typically 25 to 35% efficient. P(input) = P(output) / Efficiently = 1500 Watts/.60 = 2500Watts Transmission lines The Velocity Factor of a cable is calculated as the Velocity of the wave in the transmission line (coaxial cable) divided by the velocity of light (which is the velocity of the electrical wave in a vacuum). VF = V (transmission line) / V (light) Rev 2.00 Page 118 AD7FO’s 2012-2016 Extra Class Syllabus Since energy moves slower in a coaxial cable its electrical length will be shorter than the electrical length. A typical velocity for common coaxial cable with a polyethylene dielectric is about .66 The physical length of a typical transmission line (VF= .66) one quarter wavelength long at 14. 1 MHz would be 3.5 Meters. Physical length (PL)= [Wavelength/4] x Velocity Factor PL= [((300/14.1))/4] x .66 = [5.32] x .66 = 3.5 meters Coaxial Stubs Stub Length Shorted at far end Open at far end ¼ wave length High Impedance Low Impedance ½ wave length Low impedance High impedance Think about it as moving around the Smith Chart which is 1/2 a wavelength all the way around (180 degrees). If we move 90° on the smith chart our transmission line does the opposite of our input, so a short at 90º will appear as an open to the generator (transmitter input) end and an open will look like a short. Moving to ½ wavelength or 180º brings us back to the starting point so there is no opposite transformation, therefore a short at the output will look like a short at the input and an open will look like an open. For partial wavelengths the impedance between 0 and ¼ wavelength the line will look like an inductive reactance and for a ¼ to ½ wavelength the line will look like a capacitive reactance depending on the actual fractional wavelength. Rev 2.00 Page 119

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