# LM13700 for Variable Cutoff Freq LPF

Discussion in 'The Projects Forum' started by DanDaManJC, Nov 17, 2010.

1. ### DanDaManJC Thread Starter New Member

Oct 14, 2010
1
0
Hello All,

I'm working on designing a LPF with a variable cutoff frequency (cutoff range from 10KHz-20KHz)for a project in school. To that end, I've decided to take the OTA route since I can vary my cutoff frequency by simply changing the bias current.

In short, I plan on using the 2nd order filter stages found in this pdf:
http://129.105.69.13/datasheets/Opamps/_TransconductanceAmp_Tutorial.PDF

Figure 5a, to achieve my LPF. For the project, we need -50db/octave slope from the -3db point... so to achieve this I could simply use a chebysev filter table and cascade each 2nd order stage. In this case, I'd need 3 2nd order stages // 6 poles, using the 1.00db ripple chebysev table.

Now my question is really about constructing this thing. I've decided to use the LM13700 OTAs. Seems like the CA3280s are the OTAs of choice, but I couldnt find a good stock for quick shipping. In short, the issue is that building the circuit using the calculated values from the transfer function derived in the pdf simply don't align. Yes, that's incredibly broad, and yes, the equations aren't 100% and the real world tends to muck things up. But, let me give more detail.

There are two bias currents to set on the lm13700. The diode bias current and main bias current, henceforth ill just call that Ibias and the diode bias Id. Using the fact that, according to the LM13700 datasheet, gm ~ 19.2*Ibias, I can calculate out the C1 and C2 values per the equations in the linked pdf, choosing Ibias to be 1mA and the lower frequency at 10Khz. Choosing Ibias at 1mA would mean I'd have room to adjust up to 20Khz with Ibias, also noting Ibias and Id have max currents of 2mA. Now anyways, after calculating the values of C1 and C2 analytically... and simulating... when I don't set an Id, i receive the expected output in simulation. When I build the circuit, I'm pretty close --- nothing some manual tuning can't fix.

However! The output is severely distorted without setting Id. Apparently, the input voltage swing of the OTA is very small before we start seeing non-linearities in the output. Thus, the diodes are in there to adjust the input in such a way to make the input stay in the amplifier's linear region. So after applying Id ~ 1mA, per the reccomendation of the datasheet, I find that output is indeed non-distorted, but at the price of a pretty significantly changed frequency response.

For the sake of giving an actual example, I'll include some actual measurements.
 With Linear Diodes: -3db at: 3.8KHz with Vpp=37mV 1 octave away: 7.6KHz with Vpp=24.2mV Convert each Vpp to dB and the slope, for an octave change in freq, is 3.69dB Without Linear Diodes -3db at: 13.4KHz with Vpp=37mV 1 octave away: 26.8KHz with Vpp=20.8mV Convert each Vpp to dB and the slope, for an octave change in freq, is 5dB

So what could I do about this diode issue? I suppose I'm asking for some tips and tricks from guys that have worked with these things before. For another, what would be a good way to approach tuning this 2nd order filter? In some cases it's close to the simulated results -- but in reality it's quite a bit off.