Three experiments used in an Introductory Class in

Three experiments used in an Introductory Class in
Three experiments used in
an Introductory Class in
Electromagnetics and EMC
for Junior-Level Computer
Engineers
Presented by Professor Keith Hoover
Rose-Hulman Institute of Technology
Terre Haute, Indiana
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
1
Experiment #1
Use of Common-Mode
Choke in DC-DC
Converter Design
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
2
Goals of this experiment:
• Measure self-inductance using series-resonance method
and compare with predicted value.
• Understand operation of common-mode choke.
• Measure the self-inductance L and mutual inductance M
of a common-mode choke.
• Analyze and construct a simple dc-dc switching
converter. (This goal ties this EMC course to the
electronics courses which are prerequisite for this class.)
• Measure its conversion efficiency at different switching
rates.
• Verify common-mode choke reduces common-mode
currents on power cable of dc-dc converter.
• Observe how common-mode choke reduces radiated
emissions on ac power cord of dc-dc converter.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
3
Overview
• A homemade common-mode choke is characterized in
terms of L and M.
• A simple switching DC-DC converter is built from discrete
components, and its operation is analyzed.
• Its conversion efficiency is measured at different
switching frequencies.
• Common-mode currents flowing on the dc power cable
are measured using a current probe both with and
without the common-mode choke.
• Also, conducted emissions on the 120 VAC power line
are measured with a “Line Impedance Stabilization
Network” (LISN) both with and without the common-mode
choke.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
4
Clear benefits of using the common-mode
choke will be demonstrated using
1. Current probe to measure commonmode currents on the dc power cable
2. LISN to measure conducted emissions
on the ac power cable.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
5
Lab 1 Equipment List
–
–
–
–
–
–
2/6/2009
Agilent E4402B ESA-E Series 100 Hz – 3 GHz
Spectrum Analyzer
EMCO Model 3810/2 LISN (9 kHz – 30 MHz)
Agilent 54624A 100 MHz Digital Oscilloscope
(with 2 scope probes)
EG&G SCP-5(I)HF (125 kHz – 500 MHz) Snap On
Current Probe
Agilent E3631A Triple Output DC Power Supply
(5 V at 5 A)
Agilent 33250A 80 MHz Function Generator
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
6
Common-Mode Choke
Construction and
Measurements
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
7
Measuring L and M for a “Homemade” Common-Mode Choke
•
•
Common-mode choke constructed by bifilar winding 20 turns
of 2 strands of 20-gage hookup wire around a toroidal core.
Toroidal Core has:
–
–
–
–
Outer diameter = 2.5 cm
Inner diameter = 1.0 cm
Thickness = 0.9 cm
relative permeability µR = 5000.
A
B
20T
C
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
20T D
8
Self Inductance L of either toroidal
coil may be approximately calculated
using:
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
9
Approximate Calculation of SelfInductance “L” of either coil in choke
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
10
Experimental Measurement of Self-Inductance “L”
•
Use the series LC resonance method…Open-circuit one coil, while
other coil is resonated with a known value of capacitance.
Rgen
Lunknown
50 ohms
To Oscilloscope
1Vac
or AC Voltmeter
Cknown
Function Generator 0-80MHz
The frequency “fnull” where the signal null occurs is the frequency at which
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
11
As expected, both coils were found to have the same
fnull value, and hence both coils had the same self
inductance.
An LCR meter (Extech Model 380193) was also used to
measure the self-inductance of each coil in the
common-mode choke, and each coil read 3.51 mH on
the LCR meter.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
12
Measuring the Mutual Inductance “M”
A
B
20T
Leq(AC) = 2(L - M)
(Core flux set up by each
coil cancels)
C
20T D
Input Impedance with B-D short circuited
A
B
20T
Leq(AD) = 2(L + M)
(Core flux set up by each coil
reinforces)
C
20T D
D
Input Impedance with B-C short circuited
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
13
Finding Leq(AB)
Finding Leq(CD)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
14
Solving for L and M
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
15
Conclusions
• The closer M is to L, the better the common-mode
choke. Here L = 3.7502 mH and M = 3.7499 mH,
so they are very close!
• This common-mode choke exhibits a very low
equivalent inductance of Leq = 2*(L-M) = 600 nH
to differential mode currents (which are usually
the desired signal).
• It exhibits a much higher inductance of Leq =
2*(L+M) = 15 mH to common-mode currents due
to (the usually undesired) unintentional radiated
signal.
• Thus differential-mode signal currents are passed
more easily than the common-mode noise
currents through this common-mode choke.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
16
Simple Switching DC-DC
Converter Analysis and
Measurements
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
17
DC-DC Inverter with Common-Mode
Choke on DC Power Cable
DC Power Cable
Toroidal CT Transformer
Carries Differential-Mode Currents
& Common-Mode RF Noise Currents
A
Vin
16T
R1
15 K
6Vdc
C
32T
C3
1000 uF
16T
B
20T
Current
Probe
D1
1N4004
C1
20T D
0.01 uF
R2
15 K
+
Vout
-
RLOAD
50 ohm
Half-Wave
Rectifier with
Capacitor
Filter
C2
0.01 uF
Common-Mode Choke
Spectrum
Analyzer
2/6/2009
Common-mode choke
will be inserted and
removed from circuit
to observe its effect
on common mode
currents on the dc
power cable as
displayed on Spectrum
Analyzer.
Q1
TIP102
Q2
TIP102
Astable Push-Pull
Blocking Oscillator
fosc = 11.6 kHz
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
18
EG&G SCP-5(I)HF
(125 kHz – 500 MHz)
Snap On Current Probe
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
19
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
20
Astable Blocking Oscillator Analysis
When dc power is turned on, both
BJTs turn on equally, as baseemitter current flows through R1 and
R2. However, this is a potentially
unstable circuit (like a ball resting on
the crest of a hill). Imagine that
there is a small positive noise glitch
at the base of, say, Q2, that
suddenly makes the base current of
Q2 slightly greater than that of Q1.
This will cause Q2 to conduct more
than it was, lowering the voltage at
the collector of Q2 and (since the
voltage across C2 cannot change
instantly), lowering the base voltage
on Q1, causing Q1 to conduct less
than it was. This raises the voltage
at the collector of Q1, and this in
turn makes Q2 conduct even harder.
This positive feedback situation
quickly drives Q2 in saturation and
Q1 into cutoff.
2/6/2009
32T
Toroidal CT Transformer
16T
R1
R2
15 K
15 K
C1
0.01 uF
Vin
16T
C2
0.01 uF
6V dc
Q1
Q2
TIP102
TIP102
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
Astable Push-Pull Blocking Oscillator
fosc = 11.6 kHz
21
Astable Blocking Oscillator Analysis
However Q2 does not remain saturated and
Q1 does not remain cut off for long. This is
because C2 charges through R2, and when
C2 is charged high enough so that Vb1
exceeds Q1’s cut-in voltage, VbeCUTIN, then
Q1 turns on, and this causes Q2 to turn off.
The process then reverses, with C1
charging until Vb2 exceeds Q2’s cut-in
voltage, etc. Therefore continuous
oscillation occurs, with Q1 and Q2
alternately changing between saturation and
cut off. While Q2 is saturated during the
first half of the oscillation period, current first
flows from the center tap to the right
terminal of the toroidal transformer, and
then when Q1 saturates during the second
half of the period, current flows from the
center tap to the left terminal of the
transformer, allowing a higher voltage to be
induced in the secondary coil by transformer
action.
2/6/2009
32T
Toroidal CT Transformer
16T
R1
R2
15 K
15 K
- Vc1 +
C1 0.01 uF
Vin
6V dc
Q1
16T
Vc1
Vb1
+
Vc2
-
C2 0.01 uF
Vc2
Vb2
TIP102
TIP102
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
Q2
Astable Push-Pull Blocking Oscillator
fosc = 11.6 kHz
22
Astable Blocking Oscillator Analysis
To find the time it takes for Vb1 to increase
from its initial value to its cut in value, we
must think back to just before Q2 saturated.
At this point, the voltage on the right side of
C2 was Vin, and the voltage on the left side
of C2 was Vbe_sat. Thus just before, and
also just after, Q2 saturates,
Vc2_init = Vbe_sat – Vin
32T
Toroidal CT Transformer
16T
R2
15 K
15 K
C1 0.01 uF
6V dc
since capacitor voltage cannot change
instantly.
R1
- Vc1 +
Vin
Q1
16T
Vc1
Vb1
+
Vc2
-
C2 0.01 uF
Vc2
Vb2
TIP102
TIP102
Astable Push-Pull Blocking Oscillator
fosc = 11.6 kHz
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
Q2
23
Astable Blocking Oscillator Analysis
32T
Toroidal CT Transformer
16T
16T
R1
R2
15 K
15 K
- Vc1 +
C1 0.01 uF
+
Vc2
-
C2 0.01 uF
Vin
6V dc
Vc1
Q1
Vc2
Vb1
Q2
Vb2
TIP102
TIP102
Astable Push-Pull Blocking Oscillator
fosc = 11.6 kHz
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
24
Astable Blocking Oscillator Analysis
32T
Toroidal CT Transformer
16T
R1
R2
15 K
15 K
- Vc1 +
(Approximately)
16T
C1 0.01 uF
+
Vc2
-
C2 0.01 uF
Vin
6V dc
Vc1
Q1
Vc2
Vb1
Q2
Vb2
TIP102
TIP102
Astable Push-Pull Blocking Oscillator
fosc = 11.6 kHz
Note, the measured value of fosc was 11 kHz, so the approximate result obtained
from analysis is not accurate. This may be due to the fact that the simple analysis
above did NOT take into account the effects of the inductive load
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
25
Switching Frequency vs. DC-to-DC
Conversion Efficiency
•
•
Conversion efficiency = Pload/Pin
Conversion efficiency = (Vin*Iin)/(Vload(avg)^2/Rload)
•
2/6/2009
C1,C2 & fosc
Pin=Vin*Iin
Pout=Vload^2/Rload Eff=Pout/Pin
0.047 µF
4.33 kHz
1.85 W
1.04 W
56.1%
0.01 µF
11.6 kHz
2.14 W
1.31 W
61.1%
0.001 µF
29.1 kHz
3.19 W
1.19 W
37.1%
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
26
Vb2(t) Measurement
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
27
Vc2 Measurement
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
28
Vsecondary Measurement (50 ohm load)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
29
Vout Measurement (50 ohm load)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
30
Without Common-Mode Choke
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
31
Current Probe Spectrum 0 – 20 MHz
without Common-Mode Choke
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
32
With Common-Mode Choke Inserted
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
33
Current Probe Spectrum with
Common-Mode Choke Inserted
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
34
Conducted Emissions
Measurements
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
35
Line Isolation Stabilization
Network (LISN)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
36
LISN Spectrum (of either L1 or N
lines) W/O common-mode choke
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
37
LISN Spectrum (Either L1 or N)
with common-mode choke inserted
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
38
Experiment #2
Wireless FM
Microphone
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
39
Goals
•
•
•
•
•
•
•
Design and measure a 1.0 µH solenoidal air-core
inductor
Analyze and build an audio microphone amplifier
circuit. (This and the next two items tie this EMC
course back to the prerequisite electronics courses)
Learn about the two conditions for oscillation in a
feedback oscillator circuit.
Learn how to analyze a typical RF “LC” oscillator
circuit.
Build/debug RF oscillator, then add audio
modulation circuit to make a “wireless microphone”.
Measure Harmonic Suppression.
Experiment with radio wave propagation and
different polarizations of radiated EM waves.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
40
Equipment List
•
•
•
•
•
•
DC power supply
Agilent Spectrum Analyzer
Agilent 0 – 100 MHz Digital Oscilloscope
Agilent 0 – 20 MHz Function Generator
Portable FM radio (Walkman style or
boom box style)
Tektronix Curve Tracer
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
41
Complete Circuit of FM Wireless Microphone
Electret Microphone
Bottom View
Vcc
9Vdc
sig
Rmic
10k
gnd
Rb1
470k
Cbypass1
0.001 UF
Rc1
560 ohms
2
1.0 uH
Lx
Rb2
10k
Ccoup
Cmic
M1
Antenna (12" wire)
+9 V dc power bus
sig
gnd
Electret Microphone
0.1 UF
Cx
22 pF
1
Q2
2N3904
Cfdbk
22 pF
0.1UF
Cbypass2
0.001 UF
Q1
2N3904
Re2
1k
C B E
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
42
1 µH Inductor Design and
Measurement
• Design a 1.0 µH air-core solenoidal-wound
(single-layer) inductor.
• Use a suitable coil form (such as a felt-tip marker
pen) and insulated hookup wire.
• Recall that this inductance formula is:
N 2 µA
L=
l
Where N = Number of turns
A = cross-sectional area of coil
l = length of coil
in air µ= µ0 = 4π x 10-7 H/m
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
43
Inductor Design
We desire an inductance of
L := 1⋅ µH
I chose a coil form with diameter
d form := 0.8⋅ in
I will adjust the coil length to be
len := 1.2⋅ in
The permeability of free space (air) is
−7 H
µ := 4⋅ π⋅ 10
⋅
m
Find the cross-sectional area, A
⎛ d form ⎞
A := π⋅ ⎜
⎝ 2 ⎠
2
−4 2
A = 3.243 × 10
m
2
L
N ⋅ µ⋅ A
len
Solving for N we find N = 8.6.
Thus a coil with 9 turns and a length of 1.2 inches should yield
an inductance of about 1 µH.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
44
Measuring Actual Value of Inductor
Rgen
50 ohms
Lunknown
+
Vout
1Vac
Cknown
-
Function Generator 0-80MHz
In this case
3
Cknown := 10⋅ 10 ⋅ pF
And a series resonant amplitude null was found at
Lunknown :=
2/6/2009
1
2 2⎞
⎛ 4⋅ C
⋅
f
⋅π ⎠
known
null
⎝
fnull := 1.52⋅ MHz
−6
Lunknown = 1.096 × 10
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
H
45
Audio Amplifier Stage Analysis and Measurements
Bottom View
+9 V dc power bus
Vcc
9Vdc
sig
Rb1
470k
Rmic
gnd
10k Cmic
Cbypass1
0.001 UF
Rc1
560
Ccoup
M1
sig
gnd
Electret Microphone
0.1UF
Vaudio
0.1UF
Q1
2N3904
C B E
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
46
Beta Measurement using Curve Tracer
2/6/2009
Three Introductory EMC Expts,
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47
From Curve Tracer, β = 160
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
48
Calculation of DC Bias Q-Point of Audio Stage
To find the dc bias "Q" point, first find the quiescent base current:
Ibq :=
9⋅ V − 0.7⋅ V
−5
Ibq = 1.766 × 10
470⋅ kΩ
A
Then assuming Q1 is forward active, the collector current is
β := 160
Icq := β ⋅ Ibq
−3
Icq = 2.826 × 10
A
Therefore the Q-point of the audio stage is
−3
Icq = 2.826 × 10
and
2/6/2009
A
Vceq := 9⋅ V − Icq⋅ 560⋅ Ω
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
Vceq = 7.418V
49
Measured Q-Point of Audio Stage
• Measured Vce1q = 7.46 V (Predicted 7.42V)
• Measured Ic1q = 2.75 mA (Predicted 2.83 mA)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
50
Calculated AC Gain of Audio Stage
AC Model of Audio Stage
Collector
vo(t)
vi(t)
Base
rpi
Rc
560 ohms
Beta*ib
Emitter
ib
vo(t) = -(vi(t)/rpi)*Beta*Rc
Av = vo(t)/vi(t0 = -Beta*Rc/rpi
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
51
Calculated and Measured AC Gain of Audio Stage
rpi :=
Av
26⋅ mV
3
rpi = 1.472 × 10 Ω
Ibq
vo ( t)
−β ⋅ Rc
vi( t )
rpi
Av :=
−160⋅ 560
3
1.472⋅ 10
Av = −60.87
Measured AC gain (Using function generator in place of
microphone, set to 5 kHz and 10 mV amplitude) is
Avobserved = -52 (Calculated Av = -60.9)
Note: we used a highly simplified small-signal BJT model.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
52
Analysis of RF Oscillator Circuit
Antenna (12" wire)
+9 V dc power bus
Vcc
9Vdc
Cbypass1
0.001 UF
2
1.0 uH
Lx
Rb2
10k
Cx
22 pF
1
Q2
2N3904
Cfdbk
22 pF
Cbypass2
0.001 UF
2/6/2009
Re2
1k
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
53
DC Q-Point Calculation of Q2
• The β of Q2 was measured on the curve
tracer and found to be β = 160.
Ib2q :=
9.0⋅ V − 0.7⋅ V
10⋅ kΩ + ( 160 + 1) ⋅ 1⋅ kΩ
Ic2q := 160⋅ Ib2q
−5
Ib2q = 4.854 × 10
−3
Ic2q = 7.766 × 10
Vce2q := 9⋅ V − ( 160 + 1) ⋅ 1⋅ kΩ ⋅ Ib2q
A
A
Vce2q = 1.185V
When Vce2q was measured (first Cfdbk was removed
so that the circuit was not oscillating.) it was found that
Vce2q = 1.27 V (quite close to predicted value
of 1.185 V), and Ic2q = 7.73 mA (quite close
to the predicted value of 7.77 mA).
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
54
AC Model of RF Oscillator
• In making this model, we assume that Cbypass1 and
Cbypass2 (both 0.001 µF) act like short circuits at the 34
MHz oscillation frequency since the magnitude of the
impedance of these capacitors at 34 MHz is 1/(2π*34
MHz*0.001 µF) = 4.82 Ω!
• But note that at audio frequencies, Cbypass1 and
Cbypass2 act like open circuits, because the magnitude
of the impedance at 1 kHz is 1/(2π*1 kHz*0.001 µF) =
159.2 kΩ!
• This is important so that the audio modulating signal
applied to the base of Q2 from the audio amplifier stage is
not shorted out by Cbypass2.
• In the AC model of Q2, β = 160
• In the AC model of Q2,
rpi2 = 26 mV / Ib2q = 535.6 ohms
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
55
AC Model 34 MHz Oscillator Circuit
The base is grounded because of Cbypass2 acts like a
short circuit at the 34 MHz oscillation frequency.
B
C
2
ib2
Lx
1.0 uH
rpi2
beta2*ib2
Cfdbk
E
Cx
22 pF
1
22pF
Re2
1k
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
56
Oscillator Analysis
• Q2 functions as a “common base” amplifier.
• The input signal voltage is delivered to the
emitter terminal (E), creates a base current ib2(t)
= -vE(t)/rpi2, and the amplified output appears at
the collector terminal (C).
• Note that the output is fed back to the input via a
frequency-selective feedback network that
consists of Re2, Cfdbk, Lx, and Cx.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
57
Frequency of Oscillation set by Rx,Cx parallel
resonant (tank) circuit
Z RxCx =
1
1
j 2πfCx +
j 2πfLx
This impedance becomes infinite (acts like an open circuit) when its
denominator is set to zero
1
j 2πfCx +
=0
j 2πfLx
fres =
2/6/2009
1
2π LxCx
=
1
2π 10 −6 • 22 × 10 −12
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
= 33.93
MHz
58
A general sinusoidal feedback oscillator consists of an
amplifier and some sort of an external feedback network
A(f)
Amplifier Voltage Gain A(f)
β(f)
Feedback Network Voltage Gain β(f)
=> Loop Gain = A(f) β(f)
2/6/2009
Three Introductory EMC Expts,
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59
Conditions for Oscillation:
(a) The magnitude of the voltage gain around the loop (loop gain) is greater than 1,
so that noise at frequency “f” that is present due to the power-up transient will
be amplified to higher and higher levels as it circulates around the frequencyselective feedback loop. (The oscillations do not build up forever, since eventually
the BJT is driven into saturation or cutoff. The oscillation amplitude is self-limiting
due to device nonlinearities.)
|A(f)β(f)| > 1.0
(b) The phase shift around the loop must be an integral multiple of 2π radians, so that
the fed back sinusoidal signal will add “in phase” (constructively) with the signal
already af the input, and then oscillations can then build up.
Phase Angle [A(f)β(f)] = n2π, where n is any integer
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
60
Breaking the Feedback Loop: Loop Gain
A(f)
Amplifier Voltage Gain A(f)
Broken
Feedback
Loop
Vout
β(f)
+ Vin
Feedback Network Voltage Gain β(f)
=> Loop Gain = β(f) A(f) = Vout/Vin
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
61
Loop Gain Calculation using AC
Model of RF Oscillator
B
C
Vout(t)
2
ib2
rpi2
beta2*ib2
Cfdbk
E
Re2
1k
2/6/2009
Cx
22 pF
1.0 uH
Lx
1
22pF
Vin(t)
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
Add Rx in series with Lx to
model a “real” inductor more
accurately.
62
We may write node equations at the emitter node (VE) and the collector
node (Vout) in terms of the Laplace complex frequency variable “s”.
Then eliminating VE, we can show that
sC fdbk Re 2 β 2 ( sLx + Rx )
Vout ( s )
LoopGain =
= 2
Vin( s ) s C x Lx + sC x Rx + 1)( sC fdbk Re 2 rπ + [ rπ + ( β + 1) Re 2 ])
Replace s by j2πf and plot the magnitude and angle of the
loop gain of this circuit in order to find the frequency(s) at
which this circuit can oscillate.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
63
|Loop Gain|
Freq, Hz
Loop Gain phase shift
passes through 0
degrees at
f = 34.35146 MHz,
where the Loop Gain
amplitude is 40.30 > 1
=> circuit oscillates
Angle(Loop Gain)
(degrees)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
Freq, Hz
64
Now connect the audio stage to the RF
oscillator stage by adding Ccoup
Final Circuit
Electret Microphone
Bottom View
Vcc
9Vdc
sig
Rmic
10k
gnd
Rb1
470k
Cbypass1
0.001 UF
Rc1
560 ohms
2
1.0 uH
Lx
Rb2
10k
Ccoup
Cmic
M1
Antenna (12" wire)
+9 V dc power bus
sig
gnd
Electret Microphone
0.1 UF
Cx
22 pF
1
Q2
2N3904
Cfdbk
22 pF
0.1UF
Cbypass2
0.001 UF
Q1
2N3904
Re2
1k
C B E
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
65
Final Construction on Breadboard
Note wires must be KEPT VERY SHORT
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
66
FM Modulation Method
• The audio waveform is capacitively coupled onto
the base of RF oscillator Q2.
• This causes a small degree of base-width
modulation at the audio rate.
• This causes the collector-to-ground capacitance
of Q2 exhibited by the BJT to slightly vary at this
audio rate.
• Because Cx is in parallel with Q2’s collector-toground capacitance, this causes the resonant
frequency of the tank circuit (Lx, Cx) to be varied
slightly, and thus the oscillation frequency is
varied back and forth very slightly about the
nominal oscillation frequency at the audio rate.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
67
Oscilloscope Waveform
(Observed by VERY LIGHTLY capacitively coupling the scope probe by clipping the
probe onto the plastic wire of Lx near the collector of Q2 – if the probe is clipped directly
on the collector, it may load down the oscillator and stop oscillation)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
68
Oscilloscope Waveform Observations
• From the oscilloscope, we see that the
frequency of oscillation is near 34 MHz.
• The coil may be pulled apart or pushed
back together to alter the resonant
frequency as desired.
• Note that the waveform is quite distorted,
therefore, we expect large harmonics to be
present.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
69
Spectrum Analyzer Waveform
(observed using a 12” wire antenna connected to the input of the
Spectrum Analyzer and placed near the wireless FM microphone.)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
70
Spectrum Analyzer Observations
• Because 12” antenna wires were used on both the
spectrum analyzer and the wireless FM microphone, the
received 2nd harmonic (at 67.5 MHz) was 10 dB above
the fundamental (at 33.7 MHz).
• The 3rd harmonic (at 100.5 MHz) was 3 dB below the 2nd
harmonic
• The 4th harmonic was about equal in strength to the 3rd
harmonic
• The higher harmonics rapidly fell off in amplitude.
• We will receive the 3rd harmonic on the FM receiver.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
71
Hearing the 3rd harmonic on an FM radio
• Circuit can pick up speech clearly from 10 or
more feet away from the microphone.
• Frequency of oscillation is not very stable, since
it is determined by Lx,Cx. Moving hand near coil
will detune.
• Range of wireless microphone circuit is only
about 40 feet.
• Can experiment with different antenna
orientations and antenna lengths.
• Quarter-wave monopole would be about
(300/100)/4 = ¾ meter in length --- this should be
a good antenna length for the 3rd harmonic
signal.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
72
Is it possible to make a 102 MHz oscillator
on a breadboard possible with a “lowly”
mundane 2N3904 BJT? YES!
• Replace Lx with a SINGLE LOOP of wire
(perhaps 1.5” in length).
• Note using the scope and/or the spectrum
analyzer that the circuit still oscillates.
• Adjust the loop length for a signal in the
FM band (88 MHz – 108 MHz)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
73
102 MHz FM Wireless Microphone
NOTE: What a difference a SHORT wire can
make in an RF circuit!
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
74
Oscilloscope Waveform
(Note the freq of oscillation is now about 102 MHz.
Because this is a 100 MHz scope, the sine wave looks
“clean”…no harmonics appear to be present!)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
75
Spectrum of 102 MHz Wireless Microphone
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
76
Conclusion
The 102 MHz wireless microphone signal should
now transmit further than the 34 MHz one, since
we are now listening to the (stronger) fundamental
frequency, rather than having to listen to the 3rd
harmonic of a 34 MHz fundamental frequency!
Some team’s breadboards may not permit
oscillation directly at 102 MHz, although other
team’s breadboards (usually the ones built as
neatly as possible, with the shortest leads!) should
still function at this higher frequency!
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
77
Experiment #3
Bigger is not always
better!: Benefits of DC Power Bus
Capacitor Bypassing on Vcc(t) and
on Radiated Emissions
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
78
Equipment List
• Agilent 54624A 100 MHz Digital Oscilloscope
• Agilent E4402B Spectrum Analyzer (100 Hz – 3
GHz)
• Agilent E3631AVariable Triple Output DC Power
Supply
• Prototyping Breadboard
• Assorted capacitors with short leads (10 µF, 0.1 µF,
0.001 µF (1 nF), 100 pF)
• 74HC04 High Speed CMOS Hex Inverter
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
79
Goals
• Familiarize student with the ring oscillator, and
propagation time, rise time, and fall time
measurements.
• Allow student to investigate effects of various
types of bypass capacitors on radiated EMC
emissions.
• Allow student to investigate effects of various
types of bypass capacitors on Vcc(t) dc power
bus waveform.
• Learn how to use the spectrum analyzer/tracking
generator to model a real capacitor in terms of
an ideal capacitor in series with an ideal inductor
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
80
Part 1: Ring Oscillator
•
•
•
•
•
Construct “ring oscillator” on breadboard
Keep all leads as short and as direct as possible, as
shown in the following breadboard layout.
Connect the +5 V dc power supply lines (Vcc and
GND) to the 74HC04 hex inverter integrated circuit
using two power distribution rails on your breadboard,
Vcc = +5V at the top, and GND = 0V at the bottom, as
shown in the following photograph.
Note from this photograph how the dc power bus “ac
bypass” capacitor (Cbypass = 1 nF) is connected as
close as physically possible to the Vcc and GND pins
of the 74HC04.
Note that the capacitor should have its leads cut as
short as possible to minimize lead inductance.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
81
3-Inverter Ring Oscillator Circuit
Vout(t)
Vcc = +5 V
Cbypass
14 U1A
1
2
U1B
3
U1C
4
5
U1D
6
9
8
7
74HC04
2/6/2009
74HC04
74HC04
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
74HC04
82
Theory of operation – N-inverter Ring
Oscillator (N odd and here N=3)
• After a change at the output, it takes N*Tprop
seconds for this change to propagate back to the
output, causing the output to change state.
• Thus Tosc = 2(N*Tprop)
• Fosc = 1/Tosc = 1/(2*N*Tprop)
• Tprop = 1/(2*N*Fosc)
• Rightmost inverter is not part of ring. It is used
to “buffer” the output (reduce capacitive loading
that might slow down the final stage in the ring.)
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
83
Ring Oscillator Breadboard Layout
Note: All wires kept SHORT!
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
84
Ring Oscillator Output Waveform
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
85
Calculate Tprop of each 74HC04
inverter using the measured fosc
displayed on the oscilloscope
• 2*(3*Tprop)=1/35.34 MHz
• Tprop = 4.72 ns
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
86
Now connect five inverters in a ring, using the
sixth inverter as an isolating buffer to reduce
capacitive loading on one of the oscillating
inverters in the ring, and thereby alter the
speed of oscillation.
Use the measured value of Tprop from the 3inverter oscillator to predict the value of fosc
of the 5-inverter ring oscillator
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
87
5-inverter Ring Oscillator Waveform
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
88
Calculation of fosc from measured
value of Tprop
Predicting oscillation frequency from Tprop measured
earlier
Fosc = 1/(2*5*Tpd) = 1/(10*4.72 ns) = 21.2 MHz
This is quite close to the observed value of fosc = 21.8
MHz
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
89
Part 2. Effect of dc power
bus bypass capacitors on
radiated emissions
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
90
3-inverter ring oscillator
0-300 MHz Spectrum (12” wire antenna on spectrum
analyzer) Cbypass = 1 nF
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
91
3-inverter ring oscillator
0-300 MHz Spectrum (12” wire antenna on spectrum
analyzer) Cbypass = 100 pF
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
92
3-inverter ring oscillator
0-300 MHz Spectrum (12” wire antenna on spectrum
analyzer) Cbypass = 4.7 µF
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
93
Conclusions
• Higher value dc power bus bypass
capacitors appear to limit EMC emissions.
• But this is because these higher
capacitors permit more Vcc(t) dc pwer bus
noise glitches, which significantly slow the
rise and fall times of the output signal from
the ring oscillator.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
94
Part 3. Effect of dc
power bus bypass
capacitors on Vcc(t) dc
power bus spikes
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
95
3-inverter ring oscillator
Oscilloscope between Vcc and ground (near power
terminal) Cbypass = 100 pF.
2/6/2009
Vnoise = 20 mV pp
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
96
3-inverter ring oscillator
Oscilloscope between Vcc and ground (near power
terminal) Cbypass = 1 nF
2/6/2009
Vnoise = 29 mV pp
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
97
3-inverter ring oscillator
Oscilloscope between Vcc and ground (near power
terminal) Cbypass = 100 nF Vnoise = 26 mV
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
98
3-inverter ring oscillator
Oscilloscope between Vcc and ground (near power
terminal) Cbypass = 4.7 µF
2/6/2009
Vnoise = 28 mV
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
99
Conclusions
• 100 pF capacitor does the best job of reducing
the high-frequency Vcc(t) glitches for this 35
MHz ring oscillator.
• This results in squarer output switching
waveforms, and thus results in higher undesired
radiation
• In a general digital system that encompasses
signals of many different frequencies, probably a
parallel combination of several dc power bus
bypass capacitors would be best for reducing
Vcc(t) glitches of both high and low frequency.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
100
Part 4.
Using Spectrum Analyzer/Tracking
Generator to measure the selfresonant frequency, and also Lx,Cx
of a “real” capacitor
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
101
Tracking Generator
•
•
•
•
•
Built into our spectrum analyzer.
The spectrum analyzer’s continuously varying local oscillator (LO)
signal is mixed with the analyzer’s IF frequency.
This produces an output frequency (available to the user) that
matches, or “tracks”, the frequency to which the spectrum analyzer
is currently tuned.
Therefore if the tracking generator output (TGout) is connected
directly to the spectrum analyzer’s input (RFin), a flat horizontal line
will be traced.
If a 2-port circuit or device under test (DUT) is placed between
TGout and RFin, a “stimulus – response”, or “frequency response”
curve will be traced, allowing us to automatically measure how well
the DUT passes signals at various frequencies.
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
102
Features
Stimulus Response: Tracking Generator
Receiver
Source
DUT
Spectrum Analyzer
CRT
IF
Display
3.6 GHz BPF
LO fLO=4.6 GHz
DUT
fin=1GHz
RF in
3.6 GHz
TG out
Tracking
Adjust
Fout=4.6-3.6=1GHz
Tracking Generator
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
103
Capacitance Measurement using Spectrum Anayzer/Tracking Gen
Low Freq Model (well
below self-resonance)
High Freq Model (in the
vicinity of self-resonance)
Rgen
Rgen
50 Ohms
Vgen
50 Ohms
C1
1n
“Real Data”
recorded
using our lab
spectrum
analyzer
using a 20%
tolerance
capacitor
marked “103”
= 10000 pF =
10 nF.
2/6/2009
RL
+
Vc
C1
Vgen
L1
50 ohms
+
Vc
RL
50 Ohms
18 dB Atten
at 4 MHz
Self
Resonance
F=13.2 MHz
Linear
Frequency
Scale used!
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
104
Measuring Capacitor’s C1 & L1
Using the "Well below resonance model"
At dc ( ω = 0) the input voltage source suffers the following attenuation
as it arrives at the output terminals of the tracking generator (across the
capacitor):
Vgen ⎞
20 ⋅ log⎛⎜
⎝ Vc ⎠
⎛ 50 ⋅ Ω + 50 ⋅ Ω ⎞
AttendB 0 := 20 ⋅ log⎜
50 ⋅ Ω
⎝
⎠
AttendB 0 = 6.021
dB
AttendB 0
As ω increases from 0 to frequency " ωx", the output falls by an
additional "ArelativedB" decibels, which may be conveniently
measured using the spectrum analyzer. Thus the overall attenuation
"AttendBx" at frequency ω = ωx is given by
AttendB x
ArelativedB + AttendB 0
Gain = Vout/Vin
Attenuation = 1/Gain= Vin/Vout
ArelativedB + 6.021
2/6/2009
Vgen ⎞
20 ⋅ log⎛⎜
⎝ Vc ⎠
1
⎛
+ 50
⎜
1
⎜
+ j ⋅ ω x⋅ C1
⎜ 50
20 ⋅ log⎜
1
⎜
1
⎜
+ j ⋅ ω x ⋅C 1
50
⎝
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
⎞
⎟
⎟
⎟
⎟
⎠
105
ArelativedB + 6.021
20 ⋅ log( 2 + 50 ⋅ j ⋅ ω x⋅ C1
)
( ArelativedB+ 6.021 )
10
10
20
2 + ( 50 ⋅ ω x⋅ C1)
2
2 + ( 50 ⋅ ω x⋅ C1)
2
2
⎛ ArelativedB+ 6.021 ⎞
⎜
10
⎝
⎠
2
Important
Result that
we will use in
the lab!
ArelativedB+ 6.021
C1
2/6/2009
1
⋅ 10
50 ⋅ ω x
10
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
−4
106
Then we may use the "near resonance" model to find L1 in terms of the
resonant frequency where the output voltage amplitude passes through a
resonance "dip" that corresponds to the frequency ω = ωres at which the
impedance of "C 1 " and the impedance of the parasitic lead inductance
"L1" cancel. This frequency may be expressed in terms of L1 and C1 as
shown below:
1
j ⋅ ω res ⋅ C1
ω res
fres
2/6/2009
+ j ⋅ ω res ⋅ L1
0
1
L1 ⋅ C1
1
2 ⋅ π ⋅ L1 ⋅ C1
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
107
In our example the capacitor was marked "10 nF", and from the spectrum
analyzer display, at a frequency well below resonance (4 MHz), we measured
6 r
at
frequency
ArelativedB := 18.0 dB
ω x := 2 ⋅ π ⋅ 4 ⋅ 10
s
ArelativedB+ 6.021
1
10
C1 :=
⋅ 10
−4
50 ⋅ω x
C1 = 1.254 × 10
−8
F
(or 12.54 nF)
The self resonant frequency was observed to be 13.2 MHz, so
13.2 ⋅10
1
6
2 ⋅ π ⋅ L1 ⋅ C1
Solving for L1, we find
L1 := 11.6
2/6/2009
nH
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
108
Typical Bypass Capacitor SelfResonant Frequency and also C1,L1
Marked
Value
Lead Length
cm
Arelative
dB
100 pF
0.5
1.54
40.5
80
102 pF
10.6
1 nF
0.5
1.73
4.58
27.9
0.97 nF
33.5
1 nF
2
1.79
4.58
22.9
0.99 nF
48.7
0.1 uF
0.5
5.6
0.103
4.27
0.100 uF
13.9
0.1 uF
2
7.26
124
3.55
0.107 uF
18.8
0.33 uF
0.5
17.8
0.200
1.45
0.245 uF
49.1
0.33 uF
2
12.1
0.125
1.15
0.200 uF
96.4
2/6/2009
fres
MHz
fx
MHz
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
C1
L1
nH
109
Why was the 100 pF bypass capacitor more
effective than the 0.1 uF bypass capacitor?
• The 35 MHz ring oscillator used in this lab
causes narrow Vcc(t) power supply glitches that
repeat at a 35 MHz rate.
• A narrow 35 MHz pulse train has significant
spectral components concentrated at harmonic
frequencies of n*35 MHz, where n = 1,
2,3,4,5,…
• A real bypass capacitor can only bypass noise
harmonics that are well below its self-resonant
frequency. This is because it must exhibit
relatively low reactance (compared to the load
impedance being driven) at the noise harmonic
frequency of interest. .
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
110
• For noise harmonics below a real
capacitor’s self-resonant frequency, the
capacitor exhibits a negative (capacitive)
impedance, and thus it behaves like a
capacitor.
• For noise harmonics above its selfresonant frequency, the real capacitor
exhibits positive reactance, and thus
behaves like an inductor --- which means
the real capacitor does NOT bypass this
noise effectively
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
111
• Note that an ideal 100 pF capacitor exhibits
reasonably low reactance at even the lowest
(fundamental) noise frequency: Xc(35 MHz)
= 1/(2*Pi*35 MHz*100 pF) = 45 ohms, and
for the nth harmonic, Xc = 45/n ohms.
• Also, the “real” version of this capacitor has
a relatively high self-resonant frequency (80
MHz), so it can be expected to do a good
job filtering out at least the fundamental
frequency component (35 MHz) and the
second harmonic component (70 MHz).
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
112
• An ideal 0.1 uF capacitor has a much lower
impedance, Xc at 35 MHz, but the self-resonant
frequency of the real version of this capacitor is
only about 4 MHz, which is much lower than
even the fundamental noise frequency of 35
MHz!
• Thus even though an IDEAL version of a 0.1 uF
capacitor would do a better job than the 100 pF
capacitor in removing power supply noise,
because of its relatively low self-resonant
frequency, the real 0.1 uF capacitor is incapable
of filtering even the 35 MHz fundamental
component of the Vcc(t) noise!
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
113
When it comes to choosing a dc power
bus Bypass Capacitor…
• Conclusion:
is not
always better!
2/6/2009
Three Introductory EMC Expts,
Rose-Hulman Inst. of Tech.
114
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