Dear All,

            I'd like to know merits/demerits of leap frog structure   versus cascaed type structure.  Target filter is a 3rd Order Chebyshev Complex BPF with fc= 2MHz & 3 dB BW = 2.4 MHz. Filter type is Active RC. If you can direct to some paper or regarding material that'll be great.

Hi Dipankar,

The double terminated leapfrog structure (or ladder) shows low sensitivity to component tolerances in the PASSBAND of the filter, when implemented using purely lossless reactive components. The sensitivity is zero at the passband frequency where the passive reactance network (your filter) provides a perfect impedance match between the 2 terminations. So you are sitting at a minima as far as sensitivity to components is considered.

Note however that the sensitivity to component tolerances in the STOPBAND does not benefit from this. As a matter of fact, cascaded filters are better there for obvious reasons.

Since the theory is formulated for a passive filter, you need to make sure that the active implementation is still done in a way that allows the nice conditions and assumptions to be fulfilled, else you may not see the reduced sensitivity to components.

On a far more practical note, active leapfrog filters exhibit a very high sensitivity to design mistakes! You may never manage to debug the prototype you have made if one of your opamps runs into some trouble. Cascaded filters on the other hand are modular, and hence more forgiving. The tip which one of the authors of this paper would give you is to never make the first active filter of your career as a leapfrog.

As for references, check any decent network theory/filter design book. Good ones would be from Temes & Mitra.

Vivek

Hi Dipankar,

Re. 1: In an active RC filter realization, your opamps need to drive resistive loads. So you cannot use OTAs with high output impedance. So you need relatively low-ohmic output stages. These can be achieved using two-stage opamps, or if that is still not sufficient, with the use of a buffer stage either as the last stage of the opamp (compensation may be a bit trickier depending on how you designed your opamp), or after the OTA (poorer accuracy since buffer is not in the feedback loop).

In a cascaded structure, you should ideally see no coupling behavior between the 2 stages.

Re. 2: 100 times the cutoff frequency seems far too much. As a matter of fact, even 30 times seems slightly on the higher end. What opamp bandwidth you need to achieve depends on the requirements you have, and on the Q of your filter (the higher the Q, the more sensitive it is to imperfections). And note that small signal bandwidth is not all. Your design will also be sensitive to finite slewing in your opamp.

You need to simulate the overall filter response with realistic opamp models or with real opamps to see what bandwidth is acceptable. Remember: Your aim is to design a filter with a certain passband/stopband characteristics and a certain rolloff. You need to check how well you can achieve this.

Vivek

Hi,


I believe the requirement of loop gain GBW>100x(highest passband frequency) may be necessary in some cases. Basically this is equivalent to saying the loop gain is 40 dB at the highest passband frequency. The loop gain will affect the linearity of the filter. You also need to consider the loop gain in the stop band if you are worried about intermodulation. There are other considerations too so make sure you characterize the filter sufficiently.


cheers,
Aaron

Hi,


First let me say that i'm not really an expert in the area of filter design, but I have done some design in complex bpf before so I am aware of some of the issues.

If you only simulate AC performance, you will not be able to see the linearity of the circuit. Also, you only need a very moderate loop gain in order to get a nice looking filter curve around the passband so don't be deceived. From the AC analysis, you can generally see how high your loop gain UGB is by observing the frequency at which the transfer function of the filter starts to deviate from a "nice" looking curve. Generally speaking, op-amps can be approximated as single pole up to the unity gain bandwidth, UGB. Therefore, the higher the UGB, the higher the loop gain of the op-amp at the frequency of interest. If you don't already know, you can characterize the loop gain by performing a stb analysis in spectre.

1. It is well known that the op-amps linearity is dependent on the loop gain. The linearity can be classified by IIP3, IIP2, P1dB and THD among other parameters. Please see,

A. A. Abidi, "General Relations Between IP2, IP3, and Offsets in Differential Circuits and the Effects of Feedback" IEEE Microwave theory and techniques, vol. 51, no. 5, May 2003.

OR

W. Sansen, "Distortion in Elementary Transistor Circuits", IEEE TCAS-I, vol. 46, no. 3, March 1999.

2. I'm not sure what application you are using the ppf for, but in communications, the received signal is subject to out-of-channel interference. These interferers can intermodulate with each other due to the non-linearity of the circuit. Since they are outside of the passband of the filter, you must ensure that the linearity outside of the passband meets requirements. The linearity out of the passband can possibly be degraded by the reduced loop gain at high frequencies. On the other hand, the linearity might actually improve due to the increasing contribution of direct forward transmission of the signal through the feedback network at high frequencies. My advice is simulate the linearity for as many cases as possible.

3. As for the interstage buffers, it depends on whether the driving capability of your op-amps and the loads being driven. It will come down to loop-gain in my opinion. If the loading of the next stage severly affects the loop gain then a buffer might be necessary.


cheers,
Aaron