# SOS

The second-order-section (SOS) is an interesting circuit as it allows us to make a programmable bandpass filter. This circuit is a hassle to simulate, so here's how to do it.

## OTA-based SOS

There's many ways to make a SOS. The capacitively coupled current conveyor (C4) is one of the nicest approaches for low biases; however, I chose to make them from 9-transistor OTAs. David Graham's thesis has the details of this circuit in chapter 3.

Figure 1. The SOS constructed of OTAs.

Building off of chapter 3 in David's thesis, the capacitor values are the following:

• CW = 200fF
• C1 = 50fF
• C2 = 10fF (for simulation only, parasitics are fine in layout)
• CL = 100fF
The SOS is wrapped in a cell, and the bias voltage are mirrored in using current sources. l_tauhigh of 10nA and l_taulow of 10pA are good starting points for the currents when simulating. Figure 2 shows my setup when simulating. VDD is 5 volts.

Figure 2. The SOS cell with currents mirrored in.

### Simulating the SOS

In order to simulate the SOS with SpectreS, and by simulate I'm considering frequency sweeps to see the bandpass behavior, you must first increase the precision of the simulator. The circuit has the habit of not simulating correctly with the default tolerances. I turned my -9s to -12s. Generally, adding 3 orders of magnitude to the tolerances seems to solve this problem. The other thing which one must do is set the "vsin" source parameters appropriately.

Figure 3. The AC source (vsin) uses the parameters in the green box for AC simulations, and the red box for DC/transient simulations.

The AC source (vsin) has its "AC Magnitude" parameter set to "1 V". This allows us to easily see the behavior of the system.

Figure 4. The AC sweep configuration dialog.

The AC dialog allows you to sweep the Frequency, and the "vsin" device is the default. Click on the small image of Figure 4 above to view a larger image with my settings.

### Simulation Results

The simulation results:
Graph of response for tau_h of 10nA and tau_l of 1nA.
Graph of response for tau_h of 10nA and tau_l of 100pA.