LF: Effect of LP-filter om efficiency

[Dick Rollema <d.w.rollema@freeler.nl>]

To All from PA0SE

The following subject may have been discussed on the reflector before but
I can't remember it.

Class D and E final amplifiers have high efficiency because they produce
square waves.  When the voltage between source and  drain of
the FETs is high, current is zero; when current flows voltage is almost
zero.
But what happens if the transmitter is followed by a low pass filter with
a shunt capacitor at the input, as is often the case?
Every cycle the charge in the capacitor must be reversed and with a
current of finite value that takes some time. During that time current
flows in the conducting transistor whilst voltage over it is not small.
So one can expect dissipation in the transistor to increase and
efficiency to decrease.  

Looking at it in the frequency domain one could say that the shunt
capacitor causes the square wave to start becoming a sine wave.

If the current into or out of the capacitor is so high that charge
reversal takes negligible time, so the square wave is preserved, then
output resistance of the transmitter is obviously so small it almost puts
a short circuit over the capacitor. In that case the capacitor does
nearly nothing and could just as well be deleted...  

The problem does not arise when the LP-filter starts with a series
inductor. The sudden cut-off of current would result in  a very high
kick-back voltage at the drain of a single-ended amplifier, almost
certain killing the transistor.
But in a push pull  amplifier this is prevented by the other
transistor that starts to conduct at the same moment.
Provided of course coupling between the two halves of the primary winding
is very tight.

So it seems to me that class D and E amplifiers should preferably be
followed by a low pass filter with a series inductor at the transmitter
side. 
 
Please correct me if my conclusion is not valid.

An interesting question is whether a low pass filter is really necessary
when the transmitter feeds the aerial via a series tuning coil.
Harry Grimbergen, PA0LQ, has given this some thought and he says the
following (my translation).
Quote: 
Not unusual is an aerial capacitance of about 300 pF and a total loss
resistance in coil, aerial and earth of some 40 ohms  At 136 kHz
this results in a Q of about 100 for the aerial system. At the third
harmonic  this produces an extra attenuation of about 280 times, or
49 dB.  The third harmonic of a square wave is 9.5 dB weaker than
the basic frequency. On the other hand radiation resistance increases
with frequency squared; 9 dB for d3. 
Nevertheless harmonics will be suppressed almost 50 dB. 

About 16% of the power in a square wave is in the harmonics and this
power is reflected back into the final amplifier.
But it is not converted into heat. The DC input is decreased by this 16%
as compared to the situation where the amplifier is loaded by a resistive
load of 40 ohms for the above case.  I have been able to show this
also using simulation by MICROCAP. 
Unquote.

A problem in  The Netherlands would be that the radio inspector does
not measure harmonics as field strength but as power in the output of the
transmitter (or LP-filter, when present). So selectivity of the aerial
system does not help.

Any comments will be very welcome.

73, Dick, PA0SE