This is an article based primarily on empirical evidence, and is not the usual theoretical treatment of the subject of PA design, although it is in full agreement with the laws of physics. As such I think you will find it offers some fresh information in the spirit of amateur radio and experimentation, and will be of particular interest to QRP (10 watts SSB, 5 watts CW) aficionados.
Conventional wisdom asserts that the RF power output level from a transmitter is optimal when the impedance presented to the power amplifier is closest to its design center value. An RF output network serves to transform the typical 50 ohm load impedance to this desired PA value. But what happens when your antenna presents something other than 50 + j0 ohms to your transmitter? Most of us are aware that a transmitter load impedance specification often simply refers to a maximum tolerable VSWR value. Since there are an infinite number of impedances that fall within the typical load VSWR tolerance specification of 2.0, one might ask the question, "are some of these impedances better than others?" This article will discuss specifically how much the measured PA efficiency and RF power output level from an MFJ 9420 vary over a large set of impedances other than 50 ohms resonant, and what this means to your received signal strength. If QRP is defined as 10 watts PEP for SSB operation, it would be good to know if certain loads caused the PA to deliver more than 10 watts. For example, if you are working towards a QRP Worked All States award, but some of your QSLs were made at 11 watts, how would you feel?
The MFJ 9420 is a CW and SSB "travel radio" rated at 10 watts PEP, tuned to the 20 meter amateur radio band. Its PA consists of an MRF477 transistor operating single-ended class AB. This heat-sinked transistor is capable of dissipating 80 watts, so is not in much danger of burning up in this application, which is probably why the load VSWR spec for this radio is a relatively high 3.0. The output network of the 9420 consists of a 1:4 transformer followed by two 50:50 ohm, -90 degree pi networks (Figure 1). Thus a 50 ohm resistive load presents about 12.5 ohms to the PA. Since the phase shift across the output network is 180 degrees, any impedance at the output of the transmitter appears as that same impedance divided by 4 at the collector of the transistor (impedances repeat every 180 degrees on a lossless transmission line). This is a relatively broad-band output network, and behaves pretty much the same across the entire amateur radio 20 meter band from 14.0 to 14.35 MHz. By contrast, class C amplifier output networks have a much higher Q and tend to have a narrower bandwidth. Some amateur radio CW transmitters use a class C RF amplifier.
Usually there is some collector-to-emitter capacitance built into the PA transistor, and if this is greater than that required by the output network, it has to be parallel-resonated with an inductance, or otherwise accounted for in the design. According to the Motorola published data, the MRF477 can be modeled as about 1300 pF in parallel with 2.2 ohms when delivering 40 watts at 14.2 MHz, but since the MFJ 9420 PA is operating at only 10 watts PEP nominal, the actual parallel equivalent circuit for this condition is not specified. However the self inductance of the 1:4 transformer will tend to offset the collector capacitance, so we might assume for the moment that these "stray" reactances wash each other out, just to keep things simple. Besides, best PA performance may not occur exactly at resonance anyway. There is often a compromise between distortion, power output and efficiency.
The MRF477 is a bipolar NPN silicon transistor, or BJT. If it were an
FET, it might tend to behave as a tetrode or current source. Bipolar transistors
on the other hand are said by some to behave as a triode or voltage source,
although they may be modeled best as an exponential voltage-controlled
current source in Spice analysis. Many models assume that there are no
power supply limits, and no feedback, deliberate or stray. However in the
real world there is not much headroom designed into a transmitter power
supply, because unnecessary headroom wastes money. During these tests I
used a big power supply that actually cost more than the transmitter under
test, but at least I knew its current rating and voltage regulation were
not going to taint the results. So keep in mind that you may get different
results with an economical power supply, or with a different type of RF
power transistor. And RF feedback can very significantly alter the behavior
of a PA as the load is varied. But the main point of this article is that,
rather than relying on theoretical device models, I decided to measure
the PA performance of my MFJ 9420.
The PA has a 150 ohm stabilizing or damping resistor directly across the primary of the transformer, which pulls the 12.5 ohms down to about 11.5 ohms. This means that about 8 percent of the PA output power is wasted in the damping resistor, and 92 percent is delivered to the output network. This is a small price to pay for parasitic suppression under variable load conditions. It means that spurious emissions are minimized and PA stability is enhanced, reducing the chances of over-dissipation and failure of the transistor when operating into mismatched loads.
With no load whatsoever attached to the transmitter, I measured a PA DC current of 0.4 amps when using a 13.6 VDC supply. I ran it for 30 seconds with no problems, but would not recommend this as a common practice with other transmitters where the transistor might be running closer to its maximum ratings, or where an open-circuit at the output of the transmitter may reflect as a short-circuit at the PA (when overall output network phase shift is near an odd multiple of 90 degrees).
The PA RF choke in the power supply lead has about 0.6 ohms of DC resistance. With the key down and 13.6 volts supplied to the 9420, the RF power delivered to a 47 - j10 ohm load is about 9.0 watts. The stray reactances between the UHF connector and the printed circuit board transform this to about 48 - j5 ohms at the last capacitor in the output network. The DC input current to the radio is about 1.64 amps under these conditions, of which 0.12 amps is the quiescent current with the key up, and 0.23 amps is the current drawn by the oscillator and driver stages. This leaves 1.29 amps delivered to the PA, which means the voltage drop across the RF choke is about 0.8 volts, leaving 12.8 volts across the PA transistor. Thus the transistor input power is 12.8 volts times 1.29 amps, or about 16.5 watts, yielding an efficiency of about 54 percent at 14.25 MHz, which includes output network and damping resistor losses. If you count the loss in the choke, about 1.0 watts, the overall PA efficiency is a bit lower, about 51 percent. For the remainder of this article I will include the choke losses in the PA efficiency figures. But 51 percent is not bad for a practical class AB HF amplifier
The insertion loss of the DC ammeter in series with the PA RF choke was accounted for in the data collection. The voltage drop across this meter was almost small enough to ignore (about 0.2 volts), but I corrected the results anyway. Note that the PA bias and all other parameters were left at the factory settings through-out the testing. Using an attic dipole 30 feet off the ground, this particular 9420 received excellent SSB signal reports in Italy and Brazil from its Dallas QTH in April 1998, so the factory settings must be okay.
The power delivered to the load was determined by measuring the peak-to-peak
value of the RF waveform across the resistive portion of the load with
an oscilloscope, dividing this value by 2.82 to convert from peak-to-peak
to RMS, squaring the result, then dividing this number by the load resistance
(Equation 1). The ground side of the scope probe was always attached to
the grounded side of the resistor in the load. The reactive component in
the load was floating. The impedances were measured with a Hewlett Packard
vector impedance meter calibrated to an NBS standard. The oscilloscope
was recently calibrated in an ISO9001 lab, and its accuracy was better
than two percent. In terms of measured power, this means that the accuracy
was better than about four percent.
P = (V / 2.82 )2 / R Equation 1
The following data (Table 1) were taken with a constant 13.6 volts DC
supplied to the transceiver. Note that many 13.8 volt supplies are not
very well regulated, and often the cable between the supply and the transceiver
has a significant voltage drop across it as well when the key is down,
especially if there is an in-line fuse. When using a portable battery pack,
there will also be some sag in the voltage unless it is a large fully-charged
battery, or a good voltage regulator is built into the battery pack. The
9420 uses a number of voltage regulators on its printed circuit cards,
but the PA is connected directly to the 13.8 volt DC input and has no voltage
regulation. The 9420 is designed to operate over a supply voltage range
of 12 to 15 VDC. There is no series protective diode, only a shunt crowbar
diode and a fuseable printed circuit trace, so be careful not to hook up
your power supply leads backwards! If you add a conventional fuse, you
may find that you lose half a watt in its resistance when the key is down.
PA input PA input resistor RF load
impedance VSWR current power voltage power effic. relative field
19 + j8 ohms
2.71 1.65 A 22.4 W 30 Vpp
6.0 W 27 % 82 % -1.7
28 + j8 1.85 1.41 19.2 40 7.2 38 89 -1.0
34 + j8 1.54 1.35 18.4 44 7.2 39 89 -1.0
41 + j8 1.30 1.16 15.8 50 7.7 49 92 -0.7
47 + j8 1.22 1.09 14.8 53 7.5 51 91 -0.8
56 + j8 1.21 1.03 14.0 56 7.0 50 88 -1.1
68 + j8 1.40 0.95 12.9 58 6.2 48 83 -1.6
82 + j8 1.66 0.84 11.4 63 6.1 53 82 -1.7
100 + j8 2.02 0.79 10.7 66 5.5 51 78 -2.2
120 + j8 2.41 0.72 9.8 65 4.4 45 70 -3.1
150 + j8 3.01 0.67 9.1 68 3.9 43 66 -3.6
28 - j10 1.89 1.65 22.4 40 7.2 32 89 -1.0
34 - j10 1.57 1.55 21.1 48 8.5 40 97 -0.3
41 - j10 1.34 1.33 18.1 54 8.9 49 99 -0.1
47 - j10 1.24 1.29 17.5 58 9.0 51 100 0.0 ref
56 - j10 1.25 1.18 16.0 58 7.6 48 92 -0.7
68 - j10 1.35 1.00 13.6 59 6.4 47 84 -1.5
82 - j10 1.68 0.85 11.6 62 5.9 51 81 -1.8
100 - j10 2.03 0.82 11.2 65 5.3 47 77 -2.3
120 - j10 2.42 0.75 10.2 64 4.3 42 69 -3.2
150 - j10 3.02 0.65 8.8 66 3.7 42 64 -3.9
33 - j43 2.96 1.47 20.0 43 7.0 35 88 -1.1
47 - j43 2.37 1.30 17.7 51 6.4 36 84 -1.5
56 - j43 2.22 1.14 15.5 53 6.3 41 84 -1.5
68 - j43 2.18 1.04 14.1 55 5.6 40 79 -2.0
33 + j53 3.60 0.67 9.1 30 3.4 37 61 -4.3
47 + j53 2.85 0.71 9.7 40 4.3 44 70 -3.1
56 + j53 2.64 0.69 9.4 44 4.3 46 71 -3.0
68 + j53 2.53 0.70 9.5 49 4.4 46 71 -3.0
We can draw some general conclusions from these data. First of all one can see that the general trend per Figures 3 and 4 is towards lower power output and efficiency with increasing VSWR. It also appears that for a given VSWR, power output degrades less when the load resistance is lower than the nominal 50 ohms. However, PA efficiency and heating are both worse on this low resistance side of the Smith chart (Figure 2). I sketched in some rough constant-power curves on the Smith chart, but more data points would be required to plot these accurately. These curves form concentric rings around the maximum power output location, which is generally at the center of the Smith chart.
All of the data tend to indicate that the PA is behaving more as a voltage source than as a current source, but it is clearly not an ideal voltage source. A very stiff voltage source would produce four times as much power in a 25 ohm resistive load as it produced in a 100 ohm load. And at first glance I don't see an obvious constant source impedance value that would account for the measured results either, or that such a linear source impedance even has to exist.
Note that the correlation of PA power dissipation and efficiency with
load resistance is true both at the output of this transmitter and right
at the PA, since the phase shift across this network is 180 degrees lagging.
Therefore you could probably extrapolate this relationship to other transmitters
using other output networks, if they used the same type of PA. For example,
you would expect the opposite effect to occur in a transmitter having a
-90 degree or -270 degree output network. That is, a high output load resistance
would reflect as a low PA load resistance in such a transmitter, which
could result in possible over-heating of the PA. The idea is to translate
the load impedance from the output of the transmitter to the PA, keeping
in mind that a low PA load resistance is going to stress the PA more than
a high load resistance, at least in the MFJ 9420.
By the way, here is a trick question. Which load has a lower VSWR in a 50 ohm system: 50 + j40 ohms or 70 + j40 ohms? Did you think it was the load with the resistance closest to 50 ohms? The correct answer is 70 + j40, which has a VSWR of 2.09, as opposed to 2.18 for the 50 + j40 ohm load. Which load is better for your transmitter, assuming you don't have an adjustable impedance matching network between these loads and your PA to compensate for the mismatch? Well, you are probably going to have to measure your transmitter RF power output, input power, inter-modulation distortion and spurious RF content to fully answer that question, since all these performance criteria will vary from one transmitter to the next.
You can get a reasonable idea of the power delivered to your load by subtracting the reflected power reading from the forward power reading of your directional coupler. By the way, when was the last time you verified the accuracy of your power meter, or calibrated the impedance of your dummy load? Chances are your reflectometer, or directional-coupler, or magni-phase, or power-meter, or SWR-meter may only provide reasonable accuracy for loads close to 50 ohms. I also measured a commercial "50 ohm" ham radio load as 56 + j0 ohms at 14.25 MHz, so when in doubt, be sure to measure. A commercial dummy load may be specified as having a VSWR of 1.2 over a fixed frequency range, and may never present 50 + j0 ohms at any frequency.
You can also determine the delivered power to your load as I2R assuming you have an accurate RF ammeter and impedance measuring device, or as V2/R assuming you have an accurate RF voltmeter or oscilloscope. A calorimetric load is used by professional transmitter manufacturers, designers and broadcasters when they want a really accurate measurement of RF power output, and this requires accurate coolant flow and temperature measurement, not to mention knowledge of the specific gravity of the coolant, or humidity if the coolant is air, etc.
Unprocessed single sideband voice modulation requires less average current from the power supply than tone modulation or typical morse CW, so the PA may produce higher peak transient power outputs for SSB voice than for CW, unless your power supply is very well regulated. If the power supply voltage regulation is reasonably stiff and its current rating is conservative, the peak envelope power and CW output power may be the same. You can consider the PEP value to be the CW value over one RF cycle at the maximum level of modulation. Normal voice transients don't stick around long enough to cause the typical power supply to sag as much as it will during a key-down situation. Have you ever measured the DC voltage supplied to your PA while the key is down or your modulation density is high? How much does it sag? You might be surprised.
Since the radiated field intensity is proportional to the square-root of the power output from your transmitter, a receiver would hardly see any change in signal strength from a 9420 operating into the full range of loads within a 3.0 VSWR circle on the Smith chart according to Table 1. One S unit is typically considered to be 6 dB, and the worst relative field for the 3.0 VSWR circle data in Table 1 is 64 percent or -3.9 dB. Therefore one might conclude that as long as the reduced PA efficiency and stability are tolerable, why worry about matching the load impedance down to the nit? If you are voice modulating, the average modulation depth is relatively light compared to some other modes, and the duty cycle of a normal QSO allows the PA to cool quite a bit between transmissions. Of course, if your chosen mode has a high modulation density and high duty cycle, then you should be more concerned about mismatch. But in the case of the 9420's MRF477 PA, even with the worst-case 3.0 VSWR load you will not be operating near the power dissipation rating of this transistor.
But there are other performance considerations related to load impedance. For example, will the radio be able to modulate cleanly and fully if the power supply is already taxed by poor PA efficiency? If RF audio processing is used, will the feedback sample be degraded by a poor load? Will PA stability be okay without modulation, but degenerate with modulation when a poor load is present? When in doubt, play it safe and match that impedance.
Keep in mind that Class C and D RF power amplifiers behave quite differently from Class AB amplifiers, and every class AB transmitter has a different output network, so be careful that you don't indiscriminately apply the information contained in this article to an amplifier operating with a different amount of bias or a different set of filters and impedance matching networks.
So in conclusion it appears that when the VSWR of the load impedance presented to an MFJ 9420 is kept below 3.0, then the worst reduction in signal strength one can expect is about four dB, which is less than one S unit. Some additional good news is that if you define 10 watts PEP as an official QRP level for SSB, then you will probably never violate this limit by operating a 9420 into a mismatched load. Admittedly Figure 3 is not a terribly scientific plot of all the possible load impedances, but it does show a general trend to lead one to the conclusion that 10 watts output is only possible when the load is close to a perfect match and the power supply voltage is near 13.8 volts. The maximum RF power output I recorded was 9.0 watts for a power supply voltage of 13.6 VDC and a not quite perfect impedance match. If we assume that 10 watts is possible with a perfect match at 13.8 volts, this scales to about 12 watts at 15.0 volts, the allowed supply voltage upper limit. If we assume that the accuracy of my measurements in a worst-case scenario might be as poor as +/- ten percent of PA output power, then it might be possible to violate the 10 watt QRP limit under certain conditions. If you really want to ensure that you stay below 10 watts, crank back the supply voltage enough to allow some headroom for the resolution and accuracy of your test equipment, just in case it might be reading a bit low.
I invite the reader to make his own set of PA performance measurements
for various load conditions, and it would not surprise me if there were
certain loads that yielded a PA output power greater than that obtained
with the nominal 50 ohm resonant condition in other transmitters. Of course
this will depend on the power supply performance, the RF output network,
the type of PA transistor(s) and feedback, etc. But I think if you characterize
your transmitter's PA performance with an empirical set of data such as
I did for my little 9420, then you will know exactly what to expect. And
if you are operating QRP or looking for extra points in a contest by staying
below a certain power level, it is nice to know under what RF load conditions
you might get disqualified!
Grant Bingeman, KM5KG, is a Principal Engineer with Continental Electronics
in Dallas, Texas, where they design and manufacture high power transmitters
and antennas from DC to light. Grant has published over 100 technical articles
in various professional and trade journals. His e-mail address is DrBingo@compuserve.com.
This particular article has been published in the RSGB February 1999 RadCom