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?
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.
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).
For efficiency the transceiver output impedance is much different from its rated load impedance. For modern 100W TRX expect an output impedance of a very few Ohms.
An example: A tranceiver has a rated load impedance of 50 Ohms but an output impedance of 2 Ohms, with both impedencies purely resisitive. The output is assumed to be linear. The load is 50 Ohms resistive. If the TRX generates 52 Watts the load dissipates 50 Watts and the output device dissipates 2 Watts.
This is much more efficient than having an output impedance of 50 Ohms. To pass 50 Watts to a load would then require the output device to generate 100 Watts and dissipate 50 Watts internally. This waste of power requires almost double power from the PSU and much better cooling of the output device.
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.
