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I've often heard that the output impedance is 50Ω, and the load impedance should be matched to that and also 50Ω. While the reasons for the load impedance to be 50Ω are clear, is the output impedance really 50Ω and if so why? If it isn't 50Ω, what is it?

Wouldn't this mean a large amount of power is lost in the transmitter? Wouldn't it mean SWR losses would be much higher than they actually are?

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  • $\begingroup$ Did you mean "is the output impedance really 50Ω"? $\endgroup$ – Kevin Reid AG6YO Apr 26 '17 at 15:33
  • $\begingroup$ Yes, thanks. Edited. $\endgroup$ – Phil Frost - W8II Apr 26 '17 at 15:56
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    $\begingroup$ Cat + Pigeons! We know that the output Z of test gear - signal generator, network analyser, etc, is 50. The 100% reflection (myth) only applies to the output of an ATU. Someone who designs SSPAs needs to chime in. $\endgroup$ – tomnexus Apr 29 '17 at 21:44
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    $\begingroup$ Experiments would be hard, because the transmitter power is adjusted by the high-vswr protection circuits, so you can't trust the transmitter power to stay constant over changes in load impedance. Perhaps a very careful test of Fwd and Ref power, with impedance changed from 50 to 50+j5 to 55, keeping the SWR very low. $\endgroup$ – tomnexus Apr 29 '17 at 21:50
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    $\begingroup$ @K7PEH I recall that 75 ohms is close to optimum for minimum loss, which is why it's used for receiving cable, and 50 ohms is optimum for power handling (compromise of larger inner and the smaller gap). Now that I search for it, it's well written up here. $\endgroup$ – tomnexus May 1 '17 at 19:39
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Inside the output of a transmitter is often a PA, consisting of a transistor and a matching network. The output impedance of the transistor is easy to define during small-signal operation. From the datasheet of an MRF1535N, s22 translates to roughly 2.5-j2ohms at 100MHz. For simplicity, I'm assuming the device is unilateral, which it is not. For max gain, 50ohm would be matched to the conjugate, or 2.5+j2. The result is a transmitter with a 50ohm output impedance.

The output power and efficiency of a transistor can be optimized by maximizing the current and voltage swing at it's output. The limiting factors would be Imax and Vmax (Vbreakdown or 2*Vsupply). Loading the transistor with a resistance equal to Vmax/Imax results in a loadline capable of producing high power and efficiency.

The MRF1535N datasheet suggests a load of 1.7-j0.2, for good PA operation. 50ohm could be matched to 1.7ohm using a quarterwave line with Zo of roughly 9ohms. The result would be a transmitter with good power and efficiency into a 50ohm load. The small-signal output impedance would be 32ohm.

This is the difference between a gain (conjugate) match and a power (loadline, load-pull) match.

None of this directly answers the question, "what is the output impedance of a transmitter", because there's no simple answer. The transistor is typically operating nonlinearly, which can be modeled as a current source with a shunt RC that changes with voltage. This leads to the output impedance depending on the exact state of the PA and the exact state of the PA depending on the load.

Experts don't even agree regarding output impedance. Here's one view... "once a device starts to operate in any significantly nonlinear fashion,..., the whole concept of output impedance starts to breakdown, due to the fact the waveforms are no longer sinusoidal".

Cripps, RF Power Amplifiers For Wireless Communications, 2006.

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  • $\begingroup$ Excellent answer, thank you! Just one followup, you write: "The transistor is typically operating nonlinearly". Is this true of class AB linear amplifiers commonly used in HF transmitters for amateur radio? $\endgroup$ – Phil Frost - W8II Jun 12 '17 at 13:35
  • $\begingroup$ Class AB implies the amp is not conducting for the full cycle, but more than half the cycle. In the ideal case, the transistor is off during the rest of the cycle. The clipping when off causes AB to be nonlinear. The exact conduction angle changes with input power. An AB amp won't clip at some backed off power level. A lot of people would call this condition linear. Maybe it's where the term "linear class AB" came from. $\endgroup$ – curtis Jun 12 '17 at 17:45
  • $\begingroup$ @PhilFrost-W8II Full disclosure. I got a feel for the typical transmitter with a Google search. I'm not familiar enough with amateur radio to know how they're typically operated and at what drive levels. $\endgroup$ – curtis Jun 13 '17 at 0:37
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Strictly speaking, the output impedance of most amateur transmitters is not specified. The specifications instead state what the output power of the transmitter will be into a 50 ohm load. Often the reader will infer that this is the condition of impedance matching or a conjugate match. While a conjugate match is the condition of maximum power transfer, it is not necessarily the condition of optimum efficiency for the transmitter. It is quite common that the manufacturer of the transmitter has specified a load impedance that improves the efficiency of the transmitter in order to reduce the power supply requirements or the heat generated by the transmitter final amplifier.

With regard to the SWR question, the output impedance of the source (the transmitter in this case) does not enter into the equation for SWR which is simply based on the relationship of the load impedance (the antenna in this case) to the characteristic impedance of the transmission line.

When a source (transmitter) initially puts power into the transmission line, it is not "aware" of any mismatch of the load to the transmission line. If the load matches the characteristic impedance of the transmission line, no power is reflected so the transmitter simply sees the characteristic impedance of the transmission line. If the load impedance is not a match for the transmission line then some part of the power is reflected. The amount of power reflected is equal to the reflection coefficient squared. So for a 2:1 SWR for example, the reflection coefficient is 0.333. Square that and you find that 11.1% of the power arriving at the load will be reflected back toward the source (ignoring the losses in the transmission line for now). The power returning toward the source has the effect of altering the impedance that the source "sees" due to the forward and reflected waves combining/interacting. The exact impedance that the source sees is a function of the SWR, the frequency, and the transmission line.

For example, 50 feet of Times LMR-400 on 14 MHz with a 2:1 load will present an impedance to the source (transmitter) of 33.5 +j21 or a Z of 39.5 ohms due to the reflection. The source doesn't see this new impedance until the first reflected wave has returned to the transmitter. Of course this happens at 66% to 90% at the speed of light so the resulting change in impedance occurs seemingly instantaneously.

Tubed transmitters, due to their tunable output circuits through front panel adjustments, have the ability to have the output impedance of the tube final transformed to the impedance seen at the output connector. Thus once the reflected wave has altered the impedance that the transmitter sees, the operator can adjust the matching circuit to compensate, within a limited range, for the altered load impedance presented by the transmission line. This capability to alter the impedance matching circuit is functionally equivalent to the role of an external antenna tuner used with solid state transmitters.

A 12 volt solid state transmitter with an output power of more than a few watts, will have a final transistor amplifier circuit with a very low output impedance. In order to drive a much higher impedance 50 ohm load, the final output must be transformed through the use of an RF transformer or other suitable impedance transformation method. Since there are no operator adjustments in this output circuit like there is with a tubed final, any changes to the load impedance will alter the current through or voltage across the final transistor. Thus solid state transmitters have power foldback circuits that kick in around a 2:1 SWR in order to prevent the transistor from overheating, reaching breakdown voltage, or exceeding the maximum allowable current for the device.

Before coming back to the question of the transmitter returning the reflected power, we first need to account for the very real effect of transmission line loss. For every trip that the power takes along the length of the transmission line, some percent is lost. It is this back and forth movement of power along the transmission line that accounts for the extra loss due to a mismatched load. In the example above, each trip reduces the power by another 5.25% (-0.234 dB). So with a 100 watt transmitter, the power that reaches the load on the first trip is 94.75 watts (100 watts * 0.9475). 11.1% of this power (10.5 watts) is reflected back toward the transmitter. But this trip also experiences loss so the power returned at the transmitter is 9.97 watts (94.75 * 0.111 * 0.9475). All of these losses result in heat (the majority of the losses on HF bands are due to copper losses). We can now see that the transmitter NEVER returns all of the power reflected by the load since some of it is burned up as heat.

Does a transmitter return all available reflected power to the load? The answer is yes provided the changed output impedance presented to the transmitter (due to the reflected power) does not alter the output power of the transmitter. The power that the transmitter returns toward the load will, in the above example, again have about 10% (11.1% * 0.9575 * 0.9575) returned as measured at the transmitter. This ping-pong effect continues until all of the power is transferred or burned up as heat. Generally, within 4 to 10 trips, the amount of power bouncing back and forth has become vanishingly small.

We can empirically prove that the re-reflections by the transmitter are taking place by calculating the infinite geometric series of the losses occurring from the theoretical bouncing back and forth of the waves due to the multiple reflections and then comparing this to the actual output power of the antenna and the output power developed by the transmitter.

It is a common misconception that the output impedance of a solid state transmitter is the same as the impedance "looking into" the transmitter. As an active RF signal generator, this is rarely the case. In the lab, this condition can be met by using an attenuator of 20 dB on the output or more of the RF source. This effectively isolates the RF source from the reflected power and establishes the condition that the RF generator outputs a nearly constant RF voltage regardless of its load conditions.

The output power of a solid state transmitter will be reduced by an amount exactly equal to the power reflected from the load due to the change of input impedance of the transmission line. The reflected power is added to the output of the now reduced output power of the transmitter and sent toward the antenna (load). This meets the required condition that incident power is equal to the source power plus the reflected power. It is notable that the power output of the transmitter, before the reflected power has returned to the transmitter, is the same as the total power sent toward the antenna once the reflected power has reached the transmitter (thereby altering the input impedance of the transmission line and reducing the transmitter's output power).

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    $\begingroup$ Regarding the point of efficiency, with solid state finals the manufacturer selects a spot on the load line that satisfies or depends upon a variety of parameters including thermal resistance, maximum output voltage, or maximum current. $\endgroup$ – Glenn W9IQ Apr 27 '17 at 17:59
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    $\begingroup$ When power is reflected from the load due to its impedance mismatch with the characteristic impedance of the transmission line, what the source does with the reflected energy is not always certain. In the case where an ATU has been properly tuned we can assert that all reflected power is returned toward the load except for the attendant losses of the transmission line and tuner. Without the ATU, the reflected power changes the characteristic impedance of the load that the transmitter sees. This could result in power foldback, more power output, or a rereflection of the power toward the load. $\endgroup$ – Glenn W9IQ Apr 27 '17 at 18:00
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    $\begingroup$ Incidentally, I think it is pretty certain what happens to that reflected power: it's reflected again. It's reflected again because the transmitter has a low output impedance, and it has a low output impedance because this minimizes losses. I could be wrong, but to persuade me otherwise you'll need to answer the question, and tell me what the output impedance of a typical transmitter is. As in, with actual numbers. $\endgroup$ – Phil Frost - W8II Apr 28 '17 at 5:47
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    $\begingroup$ Agreed but this is not a high or low impedance question. A given reflection coefficient is caused by a range of complex impedances that include impedances above and below the reference impedance. For example, a reflection coefficient of 0.333 referenced to a 50 ohm line includes a load impedance of 25 ohms as well as a load impedance of 100 ohms. In other words, the characteristic impedance is at the geometric mean of all possible complex impedances for a given reflection coefficient. $\endgroup$ – Glenn W9IQ Apr 28 '17 at 18:33
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    $\begingroup$ "Does a transmitter return all available reflected power to the load? The answer is yes"... So if the answer is yes, that means the reflection coefficient is close to 1, right? What range of impedances result in a reflection coefficient of 1? Is 50 ohms among them? $\endgroup$ – Phil Frost - W8II Apr 29 '17 at 4:22
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If in the transmitter there is an impedance matching circuit and likewise a matching circuit external to the transmitter the reflected power from the load will see some kind of an impedance match not necessarily perfect such that some portion of the reflected power is consumed by the dynamic impedance of the output device such as the plate circuit of a vacuum tube or the collector of a transistor and the power going back to the antenna from the transmitter reflection will be reduced.

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