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This article looks at the nature of a valve driving a resonant load, and a method for determining the resonant load impedance for a given load line and drive conditions using a Triode in Class B grounded grid. The techniques are extensible to other valve types, other active devices and other Classes, though some of the waveform factors change.
RF amplifiers with resonant load can be operated in a range of classes which identifies the anode conduction angle with sinusoidal gridcathode drive voltage. Those of interest in this article are:
There are sub classes of AB, namely AB2 and AB1 to denote whether or not grid current flows during the input cycle.
The first three of these classes are suited to linear amplification of amplitude modulated RF waveforms such as SSB, AM etc. Most amplifiers for SSB telephony operate in Class AB, but with conduction angles that are very close to 180°, so much so that a first approximation as a Class B amplifier is a good starting point.
In the case of Class B amplifiers, the anode current with sinusoidal drive is not sinusoidal, it is a distorted sine wave.
Above in blue is a plot of the instantaneous anode current in an ideal Class B amplifier. The anode current 'pulses' rather than conducting for a whole cycle as in a Class A amplifier. The current pulses in this case flow for exactly 180° of the input cycle, and it can be seen that it resembles a rectified sine wave.
The anode current waveform contains a DC component (orange), an RF component at the frequency of the input signal (magenta), and harmonics of that frequency (not shown). The harmonics diminish in magnitude with increasing order.
The properties of this half sinusoid are used in the following analysis.
The simplest way that this anode current can be used for an RF transmitter is to use the anode current to develop power in the output circuit at the fundamental frequency and negligible output at the harmonics. What is needed is a load that offers a very low impedance at the harmonics so negigible power is developed, and a suitable resistance at the fundamental to develop the desired output power with the available voltage swing and fundamental component of current.
Valve datasheets usually contain a graph of anode characteristics. They come in two forms, both are usable for the purpose of designing the stage.
Above is the constant anode current characteristics of an Eimac 3500Z triode which will be used as an example to demonstrate an effective design process. The design objective is for 1000W RF output power from the amplifier.
The datasheet states some maximum ratings that constrain the design, the key ones are here are that maximum DC voltage is 4000V, maximum DC anode current is 0.4A and maximum anode dissipation is 500W. Limits might be stated differently in different datasheets, Ia pk, Ik RMS are other examples.
So, for the sake of this example, lets take the DC power supply to be 3150V. Note that in grounded grid operation, the valve operates at a slighly higher DC component of anode to cathode voltage as the drive voltage adds to the DC supply voltage.
Another important constraint is the minimum anode voltage. If the instantaneous anode voltage is driven too low, excessive grid current may damage the grid, and in any event, linearity is degraded. To obtain 1000W from the amplifier, anode current will need to be driven up to the high end of the curves, and it can be seen from Fig 2 that the anode current lines rapidly change slope and grid current increases rapidly below 500V anode to cathode voltage. Lets use 400V as the minimum anode voltage.
The next step is to draw a line on the anode characteristics that plots the combinations of anode voltage and grid voltage that will occur over the input cycle. This is know as a Load Line, and finding the load line can be an iterative process where the results of the first drawn load line suggests some changes and so an improved load line is drawn.
Forming the initial load line for an ideal Class B amplifier is a series of simple steps.
Anode efficiency is the ratio of RF power at the anode to DC power. Note that the DC power includes here the effect of drive voltage in a grounded grid amplifier.
We need to calculate the available voltage swing and from that the anode efficiency.
The available voltage swing in a grounded grid amplifier is the sum of DC supply voltage and peak grid  cathode drive voltage (which gives the effective DC anode to cathode voltage) less the minimum anode voltage. For the example, it can be seen that peak grid  cathode voltage is about 130V, so using the other items mentioned earlier, anode  cathode RF voltage will be 3150+130400=2880V pk.
For a perfectly linear Class B amplifier, anode efficiency equals π/4*Varfpk/Vakdc=3.14/4*2880/3280=68.9%.
To calculate the RF power at the anode for our target 1000W output, we need to make an assumption of the efficiency of the output network. For most practical HF pi couplers, efficiency should be 95% or better. Lets use 95%.
So, for 1000W output, the RF power at the anode must be the desired output power divided by the network efficiency, or 1000/0.95=1053W in this case.
We have estimated the anode efficiency, and we now know the RF power at the anode, so we can calculate the anode dissipation. It is Parf*(1/ηa1) where ηa is the anode efficiency, so 1053(1/.6891)=475W, just within the 500W maximum.
Knowing the RF power at the anode, and the voltage swing, we can calculate the peak anode current, it is 4*Parf/Varfpk=4*1053/(2880130)=1.532A. The DC component of anode current is Ipk/π=1.532/3.14=0.488A. The RF component of anode current is Ipk/2=1.532/2=0.766A.
The required resonant load impedance can be calculated from the anode RF voltage and current, Ra=Varfpk/Iarfpk=(2880130)/0.766=3590Ω.
The above information allows us to plot the intial load line on the anode characteristics. The left hand point will be at Vamin, Iapk or 400,1.5 in this case, and the right hand one at Vakdc,0, 3280,0.
Above, the initial load line plotted on the anode characteristics.
Above is a clip of a tool (Calculate initial load line of valve RF amplifier) to perform the calculations described in the foregoing text.
Note that in this case, Idc exceeds the datasheet maximum of 0.4A. If the output power requirement is respecified as 800W, Idc comes in just below 400mA for a conservative design, but the nearly 0.5mA for 1000W output is unlikely to degrade valve life in SSB telephony. The 800W output would be a better design target for high duty cycle modes.
Practical Class AB RF amplifiers depart from ideal Class B, partly due to the slightly increased conduction angle, but mostly because of the nonideal transfer characteristics of real valves.
Eimac's RF Power Amplifier Tube Performance Computer based on the work of E L Chaffee provides a method for a more practical analysis that takes into the account the valve's transfer characteristics. The method of the Eimac's RF Power Amplifier Tube Performance Computer is a bit laborious by hand and relies on some preestablished Fourier analyses. Modern computer technology provides a better solution, the same underlying method applied in a spreadsheet that calculates not just the transfer characteristic, but the Fourier analysis in real time.
The Ia/Vg transfer characteristic along the load line determined above is entered into the Characteristic Sheet.
Above is a plot of the data points (blue) and a cubic spline interpolation which will be used to calculate the anode current waveform.
Above the calculated distorted anode current waveform (blue), and the DC (orange) and RF components (magenta) calculated by Fast Fourier Transform of the anode current waveform. Grid bias has been adjusted for about 0.07mA quiescent current, and drive level adjusted for 1000W output.
Above are the calculated results from RFPATPC. Note the similarity to the figures for the ideal Class B amplifier in Fig 4, the ideal Class B analysis gives a very good estimate of the load line and some key performance characteristics. The difference depends on how closely a valve approaches ideal linearity, and how much quiescent current is added to the mix.
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