![]() We see below that the performance as simulated in SPICE is very similar to that determined in Mathematica. ( ) It could have been simulated in LTSpice, but I had a device model for the MC33284 op amp available for AIMSpice. ![]() The circuit design was simulated using AIMSpice version 2018.100. SolveĮxport Low Pass Filter 1_1 plot-``.png", n], (* it does not effect the transfer function *) (* r3 balances voltage due to input currents *) We then extract the poles of the transfer function. In this section, we determine the symbolic transfer function Vout/Vin in the s-domain of the above circuit by solving the nodal current equations. Transfer function of the Sallen-Key circuit (* impedance of parallel circuit elements *) These convenient shortcuts make the circuit equations easier to write and understand. Circuit design using Mathematica Some shortcuts Proper selection of the actual op amp makes this a reasonable approximation. For work in Mathematica, an ideal op amp will be assumed. ( ) It employs an MC33284 op amp as the active component. The circuit was drawn with LTSpice, which is a free download. The values are not duplicated: there will be two complex conjugate pairs, one pair for each stage. ![]() In this case, the pole values can be determined by using a 4th order Chebyshev1FilterModel. For example, a 4th order filter can be built by cascading two stages of the same architecture. Higher order filters can be designed by cascading stages. ![]() The design method is as follows: 1) Derive expressions for the poles of the active filter circuit in terms of the component values 2) Determine the pole numerical values using Mathematica's Chebyshev1FilterModel 3) Set the expressions for the pole values equal to the required numerical values and solve for the component values. It is the location of the poles that define the filter. This filter offers a steep cut off at the expense of some passband ripple. The filter will be a second order Chebyshev filter of type 1. This Mathematica code determines the component values for a low-pass active filter implemented using the Sallen-Key architecture. ![]()
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