R. P. HAVILAND
1035 Green Acres Circle North
Daytona Beach, FL 32119


Notes on the Conjugate Match

There has been discussion recently, (1,2, and elsewhere), about
the validity of the conjugate match theoren as applied to RF
amplifiers. Neither position in the referenced material is wrong,
but the discussions relate to two different matters.

Consider a system of two black boxes, one a transmitter, the
other an antenna, connected by a very short 50 ohm coax. The
antenna is designed to produce 50 ohms at band center, and the
transmiter is designed for connection to a 50 ohm load.

At the lower band edge the antenna impedance ZL looks like, say,
45-j30 ohms, and at the upper edge 55+j30 ohms. At band center,
design conditions exist, and the transmitter is operating as
designed. However, away from this point, the residual reactance
takes the final away from resonance, dropping output and causing
distortion and even final tube damage.

A way of compensating for this is to adjust the transmitter PI
network output capacitor to cancel the antenna reactance. This
adds 30 ohms reactance at the lower edge, and removes 30 ohms at
the upper. Resonance is now obtained by adjusting the PI network
input capacitor (frequency change also detunes the PI network).
However, the transmitter is not exactly loaded to specification,
seeing 45 ohms at the low end and 55 at the upper. Its
performance is a little below maximum, but not by a serious
amount. It could be restored to full performance by introducing
another black box, a transmatch. In essence, this takes out the
reactance, and provides a adjustable transformer to bring its
input to 50 ohms. The transmitter can always see its design load.

Note that the reactance correction was produced in all cases by
introducing a reactance of opposite sign, the conjugate of the
load reactance. This is conjugate matching, as described in
detail by Maxwell (1).

Now, within the transmitter, move to the connection between the
PI network and the output stage of the amplifier, tube or
transistor. The PI network is a impedance transformer, presenting
a resistive load RL to the output stage. The magnitude of this
load was established by the designer, when he chose circuit
values.

Bruene (2), makes the point that this load is not equal to to the
output resistance RS of the output stage, and shows some measured
values. It is true that these two resistances do not have to be
equal, but this is designers choice. If he is using a pair of
6146 tubes, it is likely that he designed for essentially maximum
output, and the PI network imput impedance will be very nearly
equal to the final stage output impedance, the maximum output
condition. But if he is using a pair of 4CX1000s, designing for
maximum tube life and minimum distortion at legal limit output,
it is likely that he intentionally used load mismatch conditions,
since he did not need maximum attainable output.

Bruene takes the position that conjugate match does not exist
unless ZL is transformed to RL equals RS, in other words, on the
simultaneous condition of reactance cancellation and attainment
of maximum output. In this he follows some (but only some) of RF
text and reference books. Others define conjugate match on the
basis of reactance cancellation alone, and separately state the
maximum output condition.

Transmitters do not have to be designed for maximum output. But
securing design operating conditions in all transmitters I have
seen does require reactance cancellation. My view is that it is
not only proper but also necessary to separate the two criteria.

I recommend that this be adopted as the amateur standard
definition.

(1) M. Walter Maxwell, Reflections, ARRL, Newington, 1990

(2) Warren Breune, RF Power Amplifiers and the Conjugate Match,
QST, v LXXV n 11, November, 1991