[hpsdr] 400w Class E linear amplifier

[Bob McGwier]

Phil Harman wrote:
> ***** High Performance Software Defined Radio Discussion List *****
>
> Horst, DL6KBF, has kindly translated DJ7AW's 400w Class E PA article into 
> English. It's at
>
> <  http://www.hamsdr.com/personaldirectory.aspx?id=739  >
>
> Many thanks Horst!
>
> 73's Phil...VK6APH
>   


Indeed,  many thanks.

The things to consider in the article as immediately relevant and of 
interest to us are the discussions concerning the envelope and phase 
channels and the group delay between them and how we can do better with 
DSP techniques in our SDR transmitters and consider the practical 
limitations he ran into.


Mathematically what is happening with envelope elimination and 
restoration transmitters could not be easier to understand if you 
consider the signals in their natural state as complex or analytic 
signals.  So we will start out immediately doing exactly that since all 
of our SDR code that is open source does this.

Consider the single sideband (for example) signal to be

i(t) + j q(t)  

where i and q are the real and imaginary signals as a function of time.

All that is happening in an EER transmitter is the conversion of this 
signal from rectangular to polar form.

i(t) + j q(t)  =   r(t) exp(j phi(t))

r(t) is the envelope or modulus.  It is found in the article by use of 
an HK-demodulator
exp( j phi(t)) is the constant envelope or "phase channel".  It is found 
in the article by a limiter.

Fortunately for us,  we can just do the computation in our software

r(t) = sqrt(i^2 + q^2)
and
phi(t) = atan2(q(t),i(t))

Since exp(j phi(t)) is constant envelope it is easily amplified by very 
very nonlinear amplifiers.   r(t) is impressed on the highly amplified 
signals by modulating collector voltage (say) of the transistors of the 
final or the final and driver.   Please note Marc Franco's notes I have 
uploaded into the repository.

I offer Nick Sokal's QEX article up for people to read from ARRL TIS:

http://www.arrl.org/tis/info/pdf/010102qex009.pdf

The thing to note about a Class E amplifier is what the current and 
voltage ideal goals are.  Hard limited voltage is on  when current is 
zero and hard limited voltage zero when current is high.   This is not 
practically possible. The extent to which it is NOT possible leads to 
the loss which decreases the efficiency from 100% to whatever the 
practical limits are.  The practical limits are determined by the 
devices and the components chosen in a class E amplifier circuit.  The 
circuit slams even harmonics into an open  or infinite load and pass odd 
harmonics unattenuated to the extent possible.   The higher the number 
of odd harmonics passed and the greater the degree to which even 
harmonics are suppressed, the closer to the theoretical 100% efficiency 
we get because the sharper the transitions from on to off and back will be.

Nick Sokal has been gracious enough to donate the Design Automation 
design and simulation suite to AMSAT.

What will our goals be?  We need to identify good parts that will pass 
lots of harmonics to get high efficiency.   The phase or hard limited 
channel and the envelope channel in the polar coordinate amplifier will 
be distorted by the circuits.  So when the amplitude is "plate 
modulated" back onto the phase signal,  these distortions will lead to 
intermodulation distortion.

With our digital signal processing there are multiple things we can do.  
We can observe and determine the appropriate pre-distortion filters to 
apply to the signals while they are still in rectangular or (I,Q) form 
so "undo" the distortions once by measurement.  Or, we can do this but 
allow for dynamic measurement to take care of any deviations.  These 
will inevitably be there because hams will not accept the need to run 
their signals into perfect dummy loads!  

I hope this helps.

73's
Bob
N4HY




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