RF Amplifier Output Voltage, Current, Power and Impedance

RF Amplifier Output Voltage, Current, Power and Impedance
RF & Wireless
RF Amplifier Output Voltage, Current, Power
and Impedance Relationship
put impedance result in a percentage of
the forward power being reflected back
to the amplifier. In some cases, excessive
reflected power can damage an amplifier
and precautions that may affect forward
power are required. Given these realities,
how does one go about determining output
voltage, current and power? Again Ohm’s
law comes to the rescue, but with the caveat
that the actual power delivered to the load
(net forward power after the application of
any VSWR protection less reflected power)
must be determined before applying Ohm’s
law. This Application note will highlight
some of the major RF amplifier characteristics that impact forward power as well as
net power allowing the use of Ohm’s law,
even when conditions are far from ideal.
Back to Basics: Ohm’s Law
Ohm’s law states that the amount of current
flowing between two points in an electrical
circuit is directly proportional to the voltage
impressed across the two points and inversely proportion to the resistance between
the points. Thus, the equation
Figure 1: Ohm’s Law pie chart
Application Note #49
Jason Smith,
Manager Applications Engineer
Pat Malloy, Sr. Applications Engineer
rf/microwave instrumentation
www.ar-worldwide.com
64
is the basic form of Ohm’s law where the
current I is in units of amperes (A), the
How much output voltage, current and power Electromotive Force (EMF) or difference
can RF amplifiers provide? This question is of electrical potential E is in volts (V), and
often asked by novice test engineers as well R is the circuit resistance given in ohms
as seasoned RF professionals. Depending (Ω). Applying the standard equation relaon the application, there is often an under- ting electrical power to voltage and current
lying desire to maximize one of the three
A
parameters: power, voltage or current. While
one would think that a simple application
of Ohm’s law is called for, this would only cross multiplying and rearranging each of
apply given ideal conditions, such as when the variables results in the equations shown
an RF amplifier with a typical 50 Ω output in the Ohm’s law pie chart (see Fig 1) shoresistance is driving a 50 Ω load. In this rare wing the various combinations of the four
case where the load impedance perfectly variables, I, V, Ω and W. Let’s use Ohm’s
matches the amplifier output impedance, pie chart to determine the output voltage,
the power delivered to the load is simply current, and power of a 50 Ω amplifier opethe rated power of the amplifier. There is rating under ideal conditions.
absolutely no reflected power and thus,
there is no need to limit or control the gain Example
of the amplifier to protect it from excessive
reflected power.
Assume we have a 100 watt amplifier with
50 Ω output impedance driving a 50 Ω load.
Unfortunately, such ideal conditions rarely This is an ideal situation in that 100% of the
apply in actual “real world” applications. forward power will be absorbed in the load
Real amplifiers are required to drive varying and therefore there is no reflected power
load impedances. The mismatch between in this example.The full 100 Watts will be
these “real” loads and the amplifier’s out- delivered to the 50 Ω load.
hf-praxis 6/2017
RF & Wireless
Selecting appropriate formulas from the tolerate a maximum power of 200 watts
Ohm’s pie chart, one can easily characte- (100 watts forward + 100 watts reverse).
rize this ideal amplifier:
Clearly this is cause for concern and amplifier designers must deal with the very real
√
possibility that the amplifier’s output might
either be accidentally shorted or the load
Substituting known values:
could be removed. Consequently, all ampli= 70,7 Vrms fiers should employ some form of protection
√
when VSWR approaches dangerous levels.
Thus, the output voltage across the 50 Ω The following is a partial list (most desirable
load is 70.7 Vrms
to least desirable) of some methods used:
Substituting known values:
= 1,41 Arms
Overdesign
• All Solid-state devices and power combiners are conservatively designed to provide sufficient ruggedness and heat dissipation to accommodate infinite VSWR.
The output load current is 1,41 Arms
• No additional active VSWR protection
circuitry is required with this approach.
As can be seen from the above example,
when impedances match, power, voltage, • This conservative approach is found on
and current are easily determined by the
AR’s low to mid power amplifiers.
application of Ohm’s law. Now let’s consider “real life” amplifiers and the effects Active monitoring of VSWR
they have on the determination of output resulting in a reduction in
voltage, current and power.
Impedance Mismatch: The
danger of impedance mismatch
and methods used to protect
amplifiers
amplifier gain when VSWR
approaches dangerous levels
Active monitoring of both
output voltage and/or current
• Limits are set for both voltage and/or current similar to restrictions placed on DC
power supplies.
• If either of the two parameters is exceeded, the amplifier is shut down.
Many amplifiers are designed with little or
no concern regarding load mismatch. It is
assumed that the application involves a load
that matches that of the amplifier. In applications like electromagnetic compatibility
(EMC) immunity testing where impedance
mismatch is the norm, care must be taken
in selecting an amplifier that can tolerate
any mismatch while still delivering the
required power.
AR solid-state amplifiers have been designed to tolerate extreme load mismatch.
They are exceptionally rugged and provide
superior protection while delivering maximum output power to any load. Impedance
mismatch is discussed in further detail in
Application Note #27A, “Importance of
Mismatch Tolerance for Amplifiers Used
in Susceptibility Testing”.
• When VSWR exceeds a safe level the for- What will be the effect of VSWR
ward power is reduced. This technique is
sometimes referred to as “gain fold-back” protection on forward power, or
power available to the load?
or just “fold-back”.
Maximum power is transferred to the load
Let’s first look at the various methods used
only when the load impedance matches the • AR’s high power solid-state amplifiers will to protect AR amplifiers from the ill effects
fold-back
when
reflected
power
reaches
amplifier’s output impedance. Unfortunately,
50% of the rated power corresponding of extreme VSWR.
this is rarely the case. In these “typical” situto a VSWR of 6:1 and will withstand any • Class A amplifiers designed to tolerate
ations, reflections occur at the load and the
amount of mismatch.
infinite VSWR: This type of amplifier
difference between the forward power and
will not fold-back or shut off when opethat delivered to the load is reflected back
rating into a high VSWR. (Most AR low
to the amplifier. A voltage standing wave is Active monitoring of VSWR
to medium power amplifiers fit in this
created by the phase addition and subtrac- leading to a shut down when
category.)
tion of the incident and reflected voltage VSWR exceeds a safe level
waveforms. Power amplifiers must either be
• This is considered a brute-force tech- • With these amplifiers, the forward power
capable of absorbing this reflected power or
is always the rated power, and is indepennique that can lead to undesirable test
they must employ some form of protection
dent of load
disruptions.
to prevent damage to the amplifier.
• Example: A 100 watt amplifier will proFor example, an open or short circuit placed • AR does not use this technique in any of
vide 100 watts forward power irrespecits
amplifiers.
on the 100 watt power amplifier discussed
tive of load variations
above would result in an infinite voltage
Active
thermal
monitoring
• Fold-back based on reflected power:
standing wave ratio (VSWR). Since
This technique is used for high power AR
• High VSWR will cause a buildup of
for Z0 >ZL and
amplifiers where the reflected power is not
heat. When a predetermined temperaallowed to exceed 50% of the rated power.
ture threshold is exceeded, the amplifier
is shut down.
• These larger amplifiers provide full rated
for ZL > Z0
power to the load for any VSWR up to
• Due to the nature of thermal time con6:1. As VSWR increases beyond this level,
stants, this approach is relatively slow.
it can be seen that VSWR is always ≥1. With
fold-back is used to limit the reflected
Extreme variations in VSWR may not
no active VSWR protection, an open circuit
power to no more than 50% of the rated
immediately result in shut down.
at the load would result in a doubling of the
power, regardless of load variations.
output voltage to 141,4 Vrms, while a short • AR amplifiers employ some degree of thercircuit would increase the output current to
mal monitoring for circuit protection but • In this case, available forward power is
equal to the rated power until a VSWR
2,82 Arms. In either of these worst case scedo not rely on this relatively slow method
of 6:1 is reached. At this point, 50% of
narios, the 100 watt power amplifier must
to protect against extreme VSWR.
hf-praxis 6/2017
65
RF & Wireless
the forward power is reflected. For any
VSWR greater than 6:1, the forward power
is reduced sufficiently to insure that the
reverse power never exceeds 50% of the
rated power.
• Example: A 1000 watt amplifier will limit
forward power to 50% of the rated power
for any load mismatch greater than 6:1.
Thus, since 500 watts is the maximum
amount of reflected power, the forward
power is 1000 watts for VSWR 6:1 and
somewhere between 1000 and 500 watts
for VSWR ≥ 6:1.
• Voltage and current limited
Figure 2: Power vs. Load Impedance 75A400
For a Voltage/Current limited amplifier,
calculations are much simpler. Ohm’s law
can be directly applied to find net power,
voltage, and load current.
The amplifier output impedance is:
For load impedance higher than the amplifier output impedance the amplifier is protected by the voltage limit. Regardless of
the load impedance the output voltage is
clamped near the specified minimum voltage rating. Applying ohm’s law:
and
Figure 3: Current vs. Voltage 75A400. (The center point of the graph occurs at the point
where the load impedance is matched to the output impedance. Maximum power is
delivered to the load only at this point)
For load impedances lower than the amplifier output impedance the amplifier is protected by the current limit. Regardless of how
small the load is, the output current will not
exceed a value near the specified minimum
current rating. Again applying ohm’s law:
=
and
xΩ
The following comments apply to amplifiers
that don’t use one of the AR style VSWR
protection methods listed above:
• Amplifiers that protect by shutting
down or turning off the RF output:
• Forward power will be 0 if VSWR is
excessive. This may occur at a VSWR as
low as 2:1, but more often occurs for a
VSWR somewhere between 2:1 and 3:1.
Figure 4: Power vs. Load Impedance 1000W1000D
66
Clearly, amplifiers that either don’t employ
VSWR protection or use this brute force
VSWR scheme cannot be used in applicahf-praxis 6/2017
RF & Wireless
tions where load mismatches are expected.
Amplifiers that employ fold-back schemes at
even lower VSWR levels than noted above
are also in this category and are unsuitable
for applications characterized by high load
VSWR such as EMC immunity testing and
research applications where load impedance
is unknown.
Output power loss due to load
mismatch
We have concentrated on the topic of forward
power up to this point. This is the power actually available at the load. Jacobi’s Law, also
known as the “maximum power theorem”
states that “Maximum power is transferred
when the internal resistance of the source
equals the resistance of the load, when the
external resistance can be varied, and the
internal resistance is constant.” This effect Figure 5: Current vs. Voltage 1000W1000D
is clearly observed when load impedance
differs (greater or less) from the amplifier’s
output impedance. As VSWR increases, an
ever greater portion of the forward power
is reflected back to the amplifier. Since
net power is calculated by subtracting the
reflected power from the forward power, it
is apparent that any VSWR other than 1:1
will reduce the actual power absorbed by
the load. The amount of power delivered to
the load can be calculated using the following standard RF formulas:
Reflection Coefficient:
The two impedances are the load impedance
and the output impedance of the amplifier.
Once the forward power has been determined and the reflection coefficient calcu- Figure 6: Power vs. Load Impedance 800A3A
lated, the net power delivered to the load
only one point where the power delivered
is found by merely substituting values into • 10 kHz – 400 MHz bandwidth
to the load is equal to the forward power;
the following equation:
• 75 Watts minimum RF output
the point where the load impedance mat• No active protection is required given its ches the amplifiers output impedance. The
fall-off of the power delivered to the load
very robust, conservative design
Furthermore, given the net power and load • Full forward power is provided into any on either side of the 50 Ω load impedance
is the result of load VSWR causing an ever
impedance one can then calculate the outload impedance
increasing portion of the forward power to
put current and voltage using Ohms law.
Figure 2 clearly demonstrates the best pos- be reflected back to the amplifier. Recall that
sible scenario provided by the 75A400. Pnet = Pfwd - Pref.
Real Examples
The forward power is constant at 75 watts
Now that we have investigated the nuances irrespective of load impedance. The center Figure 3 plots the voltage and current over
involved in determining output power, vol- point of the graph demonstrates maximum the entire range of load impedance. The
tage and current of RF power amplifiers in power transfer per Jacobi’s Law where center point represents the voltage and curgeneral, let’s look at four existing AR ampli- the 50 Ω amplifier is driving a 50 Ω load rent produced when the load impedance
fiers and how they deal with load mismatch. and the blue output power curve clearly matches the amplifiers 50 Ω output impeExample 1: Most low and medium power demonstrates the reduction in net power per dance. Loads greater than 50 Ω are plotted
amplifiers are of the Class A design and the maximum power theorem as the load to the right of the center point and loads less
have nominal 50 Ω output impedance. A varies from the ideal of 50 Ω. Note that even than 50 Ω appear to the left. The end points
typical amplifier of this type is the 75A400 though 75 watts is available independent of demonstrate the two possibilities of a worst
the load impedance (orange curve), there is case mismatch; an open where the output
power amplifier:
hf-praxis 6/2017
67
RF & Wireless
matching transformers tend to be narrow
band, this approach may prove impractical if the 1000W1000D were to be operated over its entire frequency band. In this
case, a series of narrow-band transformers
could be switched in to the application as
the frequency dictated or simpler yet, the
user could opt for a higher power amplifier.
The above graph demonstrates that even
though fold-back occurs at a VSWR of
approximately 6:1, significant output voltage
and current are still delivered to the load.
Example 3: Much has been said so far
regarding the importance of impedance
matching. The 800A3A is an example of
a unique amplifier that provides the user
with selectable output impedance to match
a wide variety of applications.
Figure 7: Current vs. Voltage 800A3A
• 10 kHz – 3 MHz bandwidth
• 800 Watts minimum output power rating
• An internal user selectable impedance
transformer provides 12.5, 25, 50, 100,
150, 200, or 400 Ω to facilitate a closer
match to the load impedance
• Active protection kicks in when VSWR
exceeds 6:1 to reduce the gain
• This fold-back protection limits the
reflected power to 400 watts maximum
The internal impedance transformer of the
800A3A allows this amplifier to have output impedance that matches that characterized by a variety of applications. External
transformers are available to extend the
usefulness of the 800A3A to include even
more applications.
Figure 8: Power vs. Load Impedance 350AH1
voltage is at a maximum with zero current,
and a short where the current is maximum
with zero voltage.
The graphs in figure 2 and 3 are based on
the minimum rated output of the amplifier
across its entire operating frequency range.
There most likely will be spots within the
frequency range where the output power will
exceed the specified minimum rated output
power. To avoid unexpected results, always
request a copy of specific production test
data before placing an amplifier in service.
• Active protection kicks in to reduce the
gain when reverse power is measured at
500 watts; this is a VSWR of 6:1 when
using the amplifier at rated power.
Figure 7 clearly highlights the benefits of
an amplifier with an internal impedance
matching transformer that facilitates a better match with varying loads. The range of
output voltage and current is considerably
greater than what is provided by a standard
50 Ω amplifier.
• This fold-back protection limits the
reflected power to 500 watts maximum
Example 4: The salient characteristics
of high power, broadband, and very low
The 1000W1000D is an example of one of output impedance (typically <1 Ω) of the
AR’s high power amplifiers that folds-back 350AH1 uniquely appeal to low frequency
when reverse power reaches 50% of rated applications. The 350AH1 differs from
power. Even though the amplifier does fold- other amplifiers in this class in that it is a
back, a considerable amount of power is still full sized bench-top instrument with “realbeing delivered to the load. In many cases, time” graphical color displays of output
other manufacturers of high power ampli- voltage and current. It’s extremely robust
Example 2: High Power Solid-State ampli- fiers would not be able to handle such con- design ensures that it can stand up to the
fiers by necessity employ active VSWR pro- ditions and forward power would either be most demanding applications.
tection. Take, for example the 1000W1000D. shut-down completely or reduced drastically. • 10 Hz – 1 MHz bandwidth
• 80 MHz – 1000 MHz bandwidth
• 1000 watts minimum RF output delivered
into a 50 Ω output impedance
68
In power critical applications, an impedance • The minimum rated output power is
350 watts into a 1.8 Ω load. This equates
matching transformer similar to the one used
to a minimum of 25 volts and 14 amps into
in the AR 800A3A could be used to match
1.8 Ω. (Power de-rated above 300 kHz)
the amplifier to the load. However, since
hf-praxis 6/2017
RF & Wireless
• Source impedance is rated at <1 Ω (Since
the output voltage and current are specified, output impedance is not used in the
forward power calculations.)
• Effective source impedance is 1.8 Ω
(Zo=Vo/Io= 25 V/14 A)
• Output protection limits both the voltage
and current at rated values into any load.
For loads less than 1.8 Ω, the output current is limited. For loads exceeding 1.8 Ω
the output voltage is limited.
This is an example of an amplifier with a
1.8 Ω effective output impedance. Due to
the voltage and current limiting protection
of the amplifier, VSWR does not play a role
in lost power delivered to the load.
Figure 9 plots the available output voltage
and current from the 350AH1. The gray area
is provided to indicate a more “typical” output profile. Individual amplifier characteristics will vary and are somewhat influenced
by operating frequency and system losses.
Figure 9: Current vs. Voltage 350AH1
from my amplifier?” can in rare cases be
answered by merely applying Ohm’s law
assuming the net power or power delivered
to the load is simply the rated power output of the amplifier. In most cases, practical
Summary
issues such as VSWR and forward power
The age old question of “How much out- concerns must be considered before appput voltage, current, and power can I expect lying Ohm’s law. While this application
note has provided guidance in this matter,
AR firmly believes that the best approach
is to apply actual test data when calculating
output parameters. If you are the least bit
uncomfortable with this exercise, feel free
to contact one of our Application Engineers.
We would be more than happy to guide you
through the process. ◄
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