# Synthetic Matching, antennas, reactance, fields

Bob Bruhns bbruhns@erols.com
Fri, 29 May 1998 07:17:01 -0400

Hal - this is an interesting subject that bears serious
examination.

When "current leads voltage by 90 degrees" in an AC circuit, it
would behave as you expect, with voltage and current exactly in
phase.

In a DC circuit, the effect is easier to see.  When you charge
a capacitor from a fixed DC voltage source, charge current is
maximum at first, when the charge is minimum - and current
gradually tapers off to zero as the rising capacitor charge
approaches the fixed supply voltage.

In an AC circuit, the capacitor is alternately charged and
discharged, and the applied voltage is alternately positive or
negative.  The capacitor voltage follows behind the charging
current, with the result that the current leads the voltage.

The zero voltage and current points are vanishingly small, and
there is no discontinuity at these points, or at the maxima or
minima.  Voltage and current pass through these points on a
smooth, continuous sine or cosine wave.

In the pressure analogy, where there is alternating pressure
and there is no flow at maximum pressure, it means the fluid is
sloshing around, so to speak.  If we have a wave going back and
forth in a bathtub, pressure is maximum when the wave crests, and
this is exactly where the net movement passes through zero as the
wave direction reverses.

The case where "voltage leads current in an AC circuit by 90
degrees" means the load is a pure inductance.  Again, the DC case
is easier to see.  Initial application of DC to an inductance
yields no current; but gradually the current increases until only
the resistance of the circuit limits its value.  With a very
low-resistance inductor and a series resistor, the voltage across
the inductor will drop from the initial DC level to nearly zero
(it would continue to approach zero if the inductor resistance
were actually zero).  If the voltage source is then disconnected,
the inductor terminal voltage can momentarily rise very high - as
many of us have accidentally discovered.  One can get an
unpleasant shock from a 1.5V battery and a fluorescent lighting
ballast in just this way.  Here we have minimum current at
maximum voltage, and maximum voltage at minimum current, but in
exactly the reverse of the capacitive case: current _lags_
voltage.

In an AC circuit, it is the load that determines the phase
relationship between voltage and current.  In RF circuits, this
(and impedance conversion and unwanted emission suppression) is
what output tuning is about.  We try to give the amplifier a
resistive load, because our amplifiers have always been designed
for this, and most of them operate inefficiently with a reactive
load.  The classic "class C" systems are analog amplifiers, and
the resistive-load coincidence of minimum voltage and minimum
current add up to minimum amplifier dissipation.  In the course
of its normal job of impedance conversion and harmonic
suppression, the output tuning circuit can also correct reactive
components of the load - but only at one frequency.

But now with switching technology we can design amplifiers
which can operate efficiently even with highly reactive loads,
meaning they can deliver wideband power to a narrowband antenna.
The amplifier device is ON or OFF, and if the circuit is designed
so that the amplifier voltage is low during the ON condition,
minimum dissipation results.  As Andre has pointed out, there are
limits to this; although theoretical efficiency is good, voltages
can get very high away from resonance, and there are physical
limits on the amplifiers.  Still, I feel this approach can
significantly increase the usable bandwidth of an
transmitter-antenna system.

Finally, antenna fields.  I think you are exactly right that an
antenna is an LC circuit with large fields.  The "lines of force"
tend to be concentrated around the antenna, but progressively
weaker ones extend further and further out, approaching zero
field at infinite distance.  Inside an ordinary capacitor, the
local lines are very strong, and the longer ones are very weak.
In an antenna we want the longer ones to be as strong as possible
because these represent signal at a distance.  If we can push
these "lines" further from the antenna, we might produce more
field at greater distances.  Similar field distortions cause
skin-effect in conductors, so this is surely possible.  Andre is
investigating one approach which I believe may be along these
"lines" right now.

Bob, WA3WDR