[Lowfer] Re: That filter can't be right!!!

[James Moritz]

At 04:01 04/09/2002 -0400, you wrote:
>Using the table and scaling equations for a 50
>ohm, .25db ripple, N=3, Chebyshev filter, for a cutoff freq of 232k, the
>inductors are 63uh and the capacitor between then to gnd is 18nf, not 1.8nf.
>I set this up in Psipe and the plotted frequency response with 50 ohm source
>and load resistances and this perfectly matches the expected response...
Dear Bill, Lowfers

Different filters do different things - the idea of Chebyshev, Butterworth 
etc filters is that you put them between two terminations and you get a 
particular frequency response. The main difference between the two types is 
the response in the passband and near the cut-off frequency - eg. the 
Chebyshev designs have a sharper cut-off. Well outside the passband, they 
are all similar; the attenuation of a low pass filter depends only on the 
number of elements in the filter, give or take a few dB.

However, these filters are not designed to maintain an impedance match - 
indeed, the attenuation and ripple is effectively produced by the impedance 
mismatch. In general, there will be a certain amount of mismatch at all but 
a few spot frequencies in the filter passband. This is not what you want 
for a PA harmonic filter, where you want a perfect match at one  specified, 
frequency, the output frequency, and high attenuation (ie. huge mismatch) 
at the harmonic frequencies. What the frequency response of the terminated 
filter will be over the total frequency range is a moot point, since only 
the TX fundamental and harmonic frequencies are actually applied, and the 
terminations provided by the PA stage and antenna are usually variable with 
frequency and non-linear, modifying the response produced anyway.

So what you really want to design is a matching network (in this case a T 
network with 2 series inductors and one shunt capacitor) that will match 
the 50ohms load to the 50ohms desired at the PA output - at the same time 
it will also act as a low pass filter. The Q of the matching network to 
some extent controls the harmonic attenuation - higher Q, higher 
attenuation, but usually you want to keep Q low to increase the bandwidth 
and make the components less critical. A typical value for Q is 1, for 
which XL = Xc = Ro, ie for 185kHz and 50 ohms,  L1 = L2 = 43.01u, C = 
17.21n. According to my simulation, this gives 14dB attenuation of the 2nd 
harmonic, 27dB attenuation of the 3rd harmonic, etc, when driven from a 
low-impedance source, as well as a 50 ohm match at 185kHz. Cascading 2 
sections like this gives a "half-wave section", which has the property that 
a mismatch at the filter output is reflected at the filter input - which 
makes tuning up easier, as well as increasing harmonic suppression.

Something else to watch when driving inductive loads using a switching 
stage - at the switching transitions, the inductance will try to force 
current to flow in the reverse direction through the switching devices - so 
commutating diodes are called for across the output devices.

Cheers, Jim Moritz
73 de M0BMU