designing low pass filters for the final stage of a transmitter

[kg4arn]

 This question is about designing low pass filters for the final stage of a transmitter.  I am familiar with designing doubly terminated filters using the tables and software applications.  But they have to be doubly terminated to perform properly.  I have built and used them successfully in small signal applications where I could control the impedance at both ends of the filter.
Take for example the circuit in the attached figure taken from Experimental Methods in RF Design.  The amplifier needs to see an approximately 7 ohms load to achieve 10W of output power.  The T matching network is used, followed by a low pass filter.  The transistor collector will see the appropriate load but the low pass filter will see the collector impedance transformed by the T network into something likely to be much higher than what is needed to meet its frequency response, if the filter is designed for 50 ohm terminations at both ends.
So at point A looking toward the low pass filter the impedance is about 7.2 ohms.  At point B looking, in the opposite direction, toward Q’s collector, the low pass filter does not see 50 ohms.  So likely that end of the low pass filter is not properly terminated.
So how do you design the low pass filter when you are not quite sure what the terminating impedance at point B will be?
 
 

[xyrtek]

Maybe I misunderstood your question but I would design the low pass filter to be 50 ohm on both sides (input and output) and do the impedance matching where required.

I can't think of any practical reason to not have the output of that very simple amplifier designed to match the load. 50 ohm for ex.

If the load (ex antenna) needs to be matched then will do that after the LPF ofc.

Per the schematic the impedance of the amplifier transistor was matched from 7.2 to 50 ohm. The LPF in that case should be 50 ohm in and out.

[T3sl4co1l]

Right, without a flat impedance on that port, the LPF won't necessarily behave as expected.

The pi network is both very frequency-selective and an impedance transformer.  So unless the LPF is narrower (in which case, we worry about its effect on the matching network instead!), we should expect it to need tuning at least.

A more comprehensive approach is to use a one-side-terminated filter prototype (assuming the collector output impedance is high -- which since this isn't grounded-base or cascode, we need to consider feedback), combined with a matching network, and to tune that for best match and response.

I did this on a small scale here,



This is a VCO + isolation/amp (grounded base) + filter + buffer:



Design concept, 95-135MHz bandpass.  Input resistance as high as possible, to maximize gain; output load resistance suitable for the output amp (a few hundred ohms, as it happens; controllable with R13 -- because that varies gain, and Miller effect, and therefore equivalent R and C seen at the base input).

Q1 collector is about 1pF || 10kohms.  This can be read off the datasheet, more or less (Ccb and Y or S params), and also meshes with my measurements (and by measurements, I mean resolving the equivalent circuit of what was built, and matching that up in the simulation).  For the desired bandwidth (40MHz), I need a load resistance less than 1/(2*pi*(40MHz)*(1pF)) ~= 4kohms, so I won't be getting maximum power gain (which would be RL = Rs, 10kohms), and I'm bandwidth limited instead.  Alright.

Then we refer to the one-port-open filter tables, and find what Zo we can get, given the known C1 (1pF) and bandwidth, and desired stopband rate (which here was around 5th order, as it happens).

For an LPF, use Fc instead of BW.  You're still getting a BP filter, really; you just might not care what the low frequency response looks like, as long as it's low enough.  Obviously, the RFC needs to be a high enough impedance over the range of interest, that it doesn't load things down, or resonate in an undesirable manner.

In my case, I opted for tuning both band edges together (a proper bandpass), hence the relatively low RFC (L1, 1uH at 95MHz is ~600 ohms!).

Next, I considered the values of the filter.  The canonical bandpass prototype has a parallel L||C, series L+C, and another parallel L||C.  The two parallel tanks aren't terrible at this impedance (100s ohms resistance, so ~100 ohms reactance at this bandwidth -- very reasonable, actually), but the series tank would have to be kohms.  To keep its impedance consistent, it would need fF of stray capacitance to ground -- impossible!

So I transformed the series capacitor into a capacitor divider, which harnesses stray capacitance, and further transforms the network impedance.

The resulting network looks like this:
L1 || (Q1_ccb) || C6 = input (shunt) tank
C6, C2, C5 = capacitor divider/transformer
(C2+C5) + L2 = mid (series) tank
C4 + L3 + C3 || (Q2 base R||C equivalent) = load LPF/tank
There's no shunt inductor on Q2 input, I think because I didn't prioritize the lower stopband as much, and various other reasons/excuses (harder to bias Q2, potential for tuned-base mode oscillation, more tuning work in general..).  The result is this:





Notice the HF stopband is better than -80dB, particularly around the 2nd and 3rd harmonic points (200-350MHz).

Ah, so, we're not done yet!  You see, we also have stray capacitance across inductors.  While I could try to ignore this, and simply get an okay stopband, I might as well harness it, and place those zeroes strategically in the stopband.  (They'll fall somewhere inevitably; hopefully at higher frequencies, >500MHz if the inductors and layout are good.)  This is where C1 and C17 come in; in the physical circuit, they are (and C2, C6 and C3) gimmicks, bits of wire or PCB soldered in and bent around until the response is right.

Zeroes, thankfully, are not a big deal to tune.  They add to the other capacitances, so those have to be tuned down slightly, but it's a much easier process than aligning a filter in the first place.

Final result: reasonable gain (as opposed to needing a beefy say ~50 ohm double terminated filter and lots more amplifier current consumption), good bandwidth, adequate flatness...



So, applying those lessons here:
- You'll need the transistor's characteristics.  This is annoying because it's class C and you need the large signal equivalent.  It may well have a low dynamic impedance (because of proximity to saturation, particularly at higher impedances), in which case a C-input filter might not even be the way to go.
- Assuming it's not saturating, it probably has a modest Zo.  Probably not as high as my grounded-base example either, because of Miller effect.  This may make it a good candidate for a filter with unequal port resistances (but not one-port-open).
- Guessing from the HAM Radio application, this doesn't need to be wide band in any way?  That tends to suggest simple L-match networks, https://www.daycounter.com/Calculators/L-Matching-Network-Calculator.phtml and coupled resonator BPFs.  This is fairly easy to design (well, as filters go), because narrow-band approximations work out.
- All of these have opportunities for impedance transformation.  The low collector load impedance suggests something in series with it, preferably an inductor* to let the harmonics do what they will on the transistor side.

*Actually, I'm not sure offhand how well this applies for BJTs at RF.  It's a good plan for class D amps.  It may be better to shunt harmonics, rather than allow them to bump around and potentially reduce the linear operating range.  Dunno.

So that would suggest an L-match (series L, parallel C), then a filter, of LPF or coupled-resonators type, with a dissimilar-dual-terminated prototype for the starting point.

Finally, run a simulation if you can, tweak values around until the response and impedance is as desired.  Build it, and go back and forth figuring out which values to adjust, and which parasitics were missing.

Or... just go with the pi network and crank it around until it works.  Whichever is best -- an in-depth design is probably not for the feint of heart, maybe "best" electrically but that doesn't matter if you never build it.

Tim

[kg4arn]

Thanks Tim.
I was hoping you would see this thread and respond.
I think I follow your example and explanation.


Ed