# Class A, AB & C Operation of Single-Ended Triode RF Power Amplifiers

Author: R.J.Edwards G4FGQ © 27th March 2002This program assists with the design of, and analyzes the performance of, triode RF power amplifiers. Cathodes are grounded. The output circuit is either a tuned tank circuit with a link coupling to a 50-ohm load, or a Pi-matching network. A Cga neutralising circuit is omitted but can be included by centre-tapping the grid tuning coil with negligible effect on other amplifier performance aspects. It is necessary to enter in this program data from tube manufacturers' sheets or characteristic curves. If users are not familiar with triode tube characteristics this program will be of educational value.

Basic Equation

Peak cathode milliamps, Ipeak = Perveance*[Vac/Mu + Vgc]^alpha

Perveance

Perveance is related to conductance. It depends on cathode surface
area, on its temperature and on the electron emitting properties of the
cathode materials. Doubling perveance is equivalent to placing two identical
tubes in parallel.

Alpha

Alpha is an exponent between 1 to 2. It sets a tube characteristics'
curvature. If alpha=1 the characteristics are linear. If 2 it is a parabola.
Theoretically alpha = 1.5 but is typically between 1.0 and 1.6
If unknown guess at 1.25

Mu

Mu is the tube's amplification factor. It is the number of times
grid voltage affects cathode current more than anode voltage. Depending
on tube geometry, Mu can lie between 3 and 150. Low Mu tubes have a lower
internal impedance and for the same power levels operate at higher currents
and lower voltages. If a tube manufacturer does not explicitly give a
value for Mu then it should be obtained by inspecting the Anode-Current
vs Grid-Voltage curves. Mu is the ratio of the anode voltage to the -ve
grid voltage needed to just cut off the anode current. It varies a little
between extremes of DC anode voltage. Use the average value.

Vac

Vac is the lowest instantaneous +ve anode voltage relative to cathode.
It is the anode DC supply volts less the peak value of the anode's RF
signal voltage.

Vgc

Vgc is the greatest instantaneous +ve grid voltage relative to cathode.
It is the peak RF signal amplitude at the grid minus the value of the
-ve grid bias.

Vac min and Vgc max occur simultaneously. Grid and anode sinewave voltages are anti-phase. Vgc must not exceed Vac or the grid will draw excessive current. The program prevents this. A large safety factor is normal, E.g., Vgc = Vac/2.

D

D is the fraction of peak cathode current which is intercepted by
the control grid. It depends on diameter and spacing of grid wires. D
tends to be smaller for small values of Mu. D affects grid RF drive power
and grid dissipation.

Anode Current Operating Angle

A complete sinewave cycle extends over a time-span of 360 degrees.
The operating angle divided by 360 is the fraction of time during which
anode current flows. At other instants grid voltage is more negative than
the anode current cut-off value, Va/Mu. A 360 degree operating angle
gives Class-A conditions. 180 to 200 degrees gives Class-AB linear
conditions. Anything less than 180 degrees is Class-C. Operating
angles for high efficiency Class-C operation vary from 80 to 150 degrees,
typically 120. Small angles offer highest efficiency but available power
output falls because cathode emission is not sufficient to provide the
short but very heavy pulses of current.

Grid Current Operating Angle

Grid current operating angle is computed - not an entered value.
Grid op-angle is considerably smaller than anode op-angle but is directly
related to it.

Entering Data

To match the characteristics of a particular tube it is not possible
to enter a suitable set of data in one operation. An initial set will
include values such as Mu, alpha, DC supply volts, op-ang, Qi, Qo, which
the user may wish to remain fixed for a time. The most important input
data are Vac(min) and Vgc(max) which set up the grid and anode signal
amplitudes. IT IS IMPORTANT TO ADJUST PERVEANCE SUCH THAT COMPUTED PEAK
ANODE AND GRID CURRENTS ACCORD WITH THE MNFR's DATA AT THE VALUES OF Vac
AND Vgc PREVIOUSLY ENTERED IN THE PROGRAM. The ratio D, grid current/cathode
current, can also be found from these values.

Modeling Tube Characteristics

Modeling tube characteristics involves inserting in the program values
of Mu, Fraction D, alpha and perveance which are proper to the tube itself
and which remain fixed while setting up operating conditions and evaluating
performance. Examine the tube's anode current versus grid or anode voltage
curves and decide whether the graphs are fairly straight or are markedly
curved. Note the anode current which flows when the anode voltage Vac
is, say, 500 volts and the grid voltage Vgc is zero. Also note the
smaller current which flows when the anode voltage is reduced to, say,
200 volts (also at zero grid volts). Note that the basic equation
is simplified by putting Vgc=0. Alpha is obtained more easily.

Now return to the program. Insert some sensible data including Mu. Set the grid voltage to zero and make a sensible guess for alpha. Set the anode voltage to 500 volts and vary perveance until peak anode current is the same value as is on the manufacturers' data sheets. Then reduce anode voltage to 200 volts and check peak anode current falls to the lower manufacturer's value. If not, then READJUST ALPHA AND REPEAT READJUSTMENT OF PERVEANCE UNTIL THE PROGRAM TRACKS THE ANODE CURRENT VERSUS ANODE VOLTAGE CHARACTERISTIC BY VARYING ANODE VOLTAGE ONLY with Vgrid=0.

The foregoing must be done using PEAK anode or cathode currents. However, tube performance is insensitive to small changes in curvature. So perveance should always be the last parameter to be adjusted. Grid and anode signal amplitudes can then be adjusted independently of basic tube characteristics.

The fraction D of cathode current drawn to the grid is small when Mu is smaller than about 15 and when Vgc is small relative to Vac it is crudely in the range 0.01 to 0.07 For medium values of Mu, say 15 to 60, D is crudely 0.07 to 0.25. For high Mu values, and when Vgc is not much smaller than Vac, D can be as high as 0.25 to 0.4 In general, in higher power tubes due to secondary emission at the grid, grid current is an uncertain quantity. It is necessary to allow considerable latitude in grid drive power requirements. But do not overlook Fraction D in this program.

Manufacturers do not have a standard method of presenting tube data. But always look for grid and anode currents which flow at Vgc max and Vac min. If not available all is not lost. Estimate perveance and alpha such that computed performance matches manufacturer's claimed data including drive power, anode loss and power output under one set of conditions. Other conditions can then be investigated.

The Pi-tank circuit matches to 50-ohms. When the tune capacitor has the same C as the LC tank both circuits have the same operating Q. If the tune capacitors differ then the Pi-tank has a higher Q than asked for because in some circumstances a low Q may not be possible. But the computed 50-ohm match is always OK. Note that a choke-capacitor coupling is needed between anode and Pi-network.

The tuned anode tank has a link-coupling to a 50-ohm load resistance. The link is assumed to be placed over the cold RF end of the tank coil. Computed step-down turns ratio is an approximation. The number of turns on the link may need to be increased relative to the number of turns on the tank coil.

Before finalising a design check all input and output data items. Always check anode and grid dissipations are within their specified ratings. If dissipation is too high reduce either or both Vgc max and Vac min.

Negative grid bias is obtained from DC grid current flowing through a resistor. If a DC power supply of the same voltage is used set R = 0. Computed RF drive power, peak signal volts, grid dissipation, etc., will remain unchanged. It is assumed the bias resistor is RF-bypassed when computing grid input impedance.

3-500Z

The 3-500Z is a high-Mu triode. On hitting T it is first set up as
a high efficiency Class-C, grounded-cathode amplifier. Reduce the DC supply
to 3000 volts and change op-angle to 201 degrees to convert
to a Class-AB2 zero-bias linear amplifier. Max ratings: Anode=500 watts,
4000 VDC, 0.4 amps DC, Grid=20 watts

L(owMu)

L(owMu) uses a small, low-Mu, receiving-type tube as an efficient Class-C power amplifier or power oscillator.

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