Active low-pass filters --- good to what frequencies?

Question

Appendix E of The Art of Electronics, 3rd Edition (LC Butterworth filters) starts by saying that "active filters are convenient at low-frequencies but impractical at higher frequencies". They go and say that "at frequencies of 100kHz and above, the best approach is passive LC filters" (paraphrased in both cases).

My first question: really? A mere 100kHz is already too high for active filters to be practical?

I understand that op-amps with high bandwidth and HIGH slew-rate can be pricey, making it "impractical" in the general case --- however, a low-pass LC filter with, say, 1MHz cutoff, T topology with a 1kΩ load ends up requiring inductors in the order of hundreds of μH --- if I need to avoid distortion (magnetic core saturation and hysteresis), an air-core inductor in that range makes the whole thing rather impractical.

Question 2 would be: is a cutoff frequency of, say, less than 10MHz too high for a Sallen-Key 2nd-order low-pass filter?

^{simulate this circuit – Schematic created using CircuitLab}

Analyzing it from the perspective of the ideal case (assuming op-amp always within linear operation), all three pins of the op-amp will be subject to the low-passed output signal --- at < 10MHz cutoff frequency that's certainly not an issue (neither bandwidth nor slew rate). Input capacitance shouldn't be a big issue --- with R in the order of 1k, the capacitors are in the order of a few tens of pF to a few hundreds of pF --- high enough to make the op-amp's input capacitance negligible.

Are there any other practical issues that I'm overlooking? Am I being realistic if I want such an active filter with cutoff in the order of a few MHz? (pricing is not an issue --- if I need an op-amp in the $10 or $20 range, that's fine)

Answer 1

I believe your analysis to be good. I've made sallen-key 4th order filters that cut-off around 3 MHz with absolutely no worry about performance. I don't see that 10 MHz is unachievable.

It's all about op-amp choice. For a unity gain stage it's easy to ascertain where the gain starts dropping below (say) 0.99 and regard that as the limiting frequency. On the other hand, the output impedance of an op-amp usually gets worse as it enters the MHz regions so you have to be sure it can deliver the peak current without clipping or going too sloppy.

You also have to consider slew rate limitations but, as far as I'm aware, that's about it.

It's quite possible that The Art of Electronics, 3rd Edition didn't make any updates on that section since it first came out in 1980.

Answer 2

My first question: really? A mere 100kHz is already too high for active filters to be practical?

No, 100kHz is nothing, but it all depends on the opamp. At some point the Gain Bandwidth Product is going to cause problems. If you had an op amp with a 1MHz or 10MHz GBWP (which may have been typical at the time of the first edition of AofE, maybe they didn't update it is my thinking so I'd compare editions) then 100kHz doesn't sound too unreasonable, because you'd only get a magnitude or two of filtering and then the bandwidth goes below unity gain. Then your lowpass filter looks more like a bandpass.

Are there any other practical issues that I'm overlooking? Am I being realistic if I want such an active filter with cutoff in the order of a few MHz? (pricing is not an issue --- if I need an op-amp in the $10 or $20 range, that's fine)

If you really do need filtering past 50MHz then parasitics need to be modeled as ESR and ESL in capacitors will start to affect the filter poles and create their own filter poles at high frequencies. Use a spice package if possible. Make sure the GBWP is high enough, these days it's not hard to get op amps that work in the +100MHz range.

Answer 3

The main problem with that Sallen Key topology at high frequency is that the output impedance of op-amps rises, so fails to control feedforward of the input signal through the 2C capacitor, trashing the stopband.

Answer 4

TI has a 10MHz design App Note. It is based on their THS4001 low-cost 270 MHz -3dB Op Amp.

Op Amps have an open loop output impedance much higher than your 50 Ω signal generator. This makes them stable with their short circuit protection. The higher GBW is used to lower the Zout = Zoc/GBW. The breadboard ESL (0.5nH/mm) and stray capacitance will need to be minimized.

With 150 MHz GBW you can use 1k R's with 5 pf, 10pF.

I did not read their design.

http://www.ti.com.cn/cn/lit/an/sloa032/sloa032.pdf

To design any filter, you should consider these specs 1st;

Source impedance \$Z_S(f)\$   
Load Impedance \$Z_L(f)\$   
Gain   -3 dB passband \$f_p\$    
Loss   @ \$f_s\$stop band edge   e.g. \$  ~-dB~ @ ~2*f_p, 10*f_p\$    
 ..  or order of filter    
% load regulation error = % Output/Load impedance ratio ( for low % )    
Phase shift in passband, group delay  
Noise, supply power  
Output swing and slew rate limit