# Pi coupling a single ended valve RF Power Amplifier

The traditional explanation of how a RF Power Amplifier (PA) tank circuit operates as a kind of flywheel, with energy being supplied to it at the desired output frequency by the output valve is a simplistic explanation that does not provide an adequate explanation for a PA designer, more later.

This article offers a better model for understanding the very popular single ended valve PA with low pass pi coupler.

# Spectral content of anode current

The article Spectral content of anode current in Class B/AB RF amplifier explains that the anode current waveform in a single ended Class AB or B RF power amplifier has a DC component, and AC components that include fundamental and its harmonics.

Good transmitters should have very low output power on other than the desired frequency. The Australian Amateur Licence Conditions Determination limits spurious emissions from high power amateur HF transmitters to at least 50dB (or 0.001%) below Peak Envelope Power.

The PA output circuit serves as a filter to ensure that the DC and harmonic components of anode current greatly reduced at the PA output terminals.

# The output circuit is a filter

The role of the PA output circuit is to:

1. separate the DC component and route it to the power supply;
2. to transform the external load to the desired anode load impedance; and
3. to offer very low anode load impedance to the harmonics.

Separating the DC component (1) is a fairly easy task, though some practical design issues to ensure that should the isolating capacitor fail, there is a DC path to ground to ensure that the HV fuse blows rather than allow HV to appear on the PA output terminals.

Transforming the external load to the desired anode load impedance (2) is not a very complex problem, except that the same filter sections must also offer very low anode load impedance to the harmonics (3).

Objective 2 could also be views as transforming the fundamental component of current at the anode into the current required in the external load to develop approximately the same power. So, if the fundamental component of anode current is 1A in a stage capable of 1000W RF output, then for a 50Ω external load I=(1000/50)^0.5=4.5A.

In a similar way objective 3 could also be views as transforming the fundamental component of current at the anode into the current required in the external load to develop a much lower power, less than 0.001% is a good target.

Thinking of the output network in terms of current is a good approach to understanding its behaviour and design. (Analyses that voltage drive the network underestimate harmonic reduction and sensitivity of harmonic reduction to Q.)

# Choosing component values

## Loaded Q

A pi coupler can perform the desired impedance transformation at the fundamental frequency using a range of combinations of L and Cs, which raises the question of whether some combinations are better than others.

One of the operating parameters of a pi section is the loaded Q. A particular combination of L and Cs gives rise to a particular loaded Q. Guidelines for transmitter design often suggest Q ranging from 12 to 15, but many hams will counter with proof that their transmitters 'work' with Q of 8 and lower.

## The second harmonic

The harmonics decrease in amplitude as they increase in order, the second harmonic is the most troublesome because:

•  it is highest in amplitude; and
•  being nearest to the desired frequency is harder to filter effectively.

The second harmonic component of anode current depends on angle of conduction of the valve and linearity of the valve transfer characteristic. For an ideal Class B single ended stage, the second harmonic component is about 7.5dB below (42%) the fundamental current. Practical Class AB and B PAs with have second harmonic current very close to 7.5dB below (42%) the fundamental current.

So, if the second harmonic needs to be at least 50dB down in the load, the pi section must attenuate the second harmonic current by some 43dB. That is no small task for a single section filter!

# Pi network

This section presents behavior of a modelled pi network designed to transform a 50Ω external load to 1500Ω anode load. In this model, the capacitors are taken to be lossless (a fair assumption for air spaced capacitors), Q of the inductor is taken to be 300 at the fundamental, and increases proportional to square root of frequency.

Network behavior for transformations other than the modelled 1500Ω/50Ω will vary, but the concepts are applicable

Fig 1 above shows the efficiency of the pi network for this scenario for a range in loaded Q. Efficiency can be improved by using an inductor with lower loss.

Fig 2 above shows the second harmonic output relative to the fundamental for a range of loaded Q for a network designed to transform a 50Ω external load to 1500Ω anode load. In this model, the capacitors are taken to be lossless, Q of the inductor is taken to be 300 at the fundamental, and increases proportional to square root of frequency.

It can be seen that harmonic output reduces quite quickly for increasing Q up to about 12 to 15, a 10dB reduction is available from Q=6 to Q=12. (CPI/Eimac 2003, p52) recommends Q=15 as a compromise between harmonic reduction and network efficiency.

Note that with a Q of 12, the harmonic output at -45dBc is still 5dB short of the target. As mentioned earlier, many hams insist that Q=8 is more than sufficient, and harmonic output is some 5dB worse than a network with Q=12 in this scenario.

# The flywheel model

The flywheel model of the tuned RF amplifier, eg (Measures 1998), (Wilson 2007, p18.3), gives but a shallow understanding, it does not provide the basis for designing an output network that meets any specific spurious radiation requirement.

# Links / References

• CPI/Eimac. 2003. Care and Feeding of Power Grid Tubes 5th Edition.
• Measures, Richard. Nov 1998. Amplifiers, Part 1. http://www.somis.org/D-amplifiers1.html (accessed 24/09/11).
• Wilson, Mark ed. 2007. ARRL Handbook. Connecticut: The American Radio Relay League.
• Calculate RF amplifier pi coupler

# Changes

 Version Date Description 1.01 28/05/11 Initial

© Copyright: Owen Duffy 1995, 2017. All rights reserved. Disclaimer.