BPF PoleZero (Bandpass Filter, Pole Zero)

BPF_PoleZero (Bandpass Filter, Pole Zero)

Symbol

Available in ADS and RFDE

Parameters

Notes/Equations

1. This is an S-domain filter.
2. Denominator and Numerator are a list of polynomial coefficients.
   The transfer function for the filter is:
   
   where
   S = j ×  (Freq/F_o − F_o /Freq)/(F_high/F_o − F_o /F_high )
   and
   Freq is the analysis frequency
   Fhigh = Fcenter + 0.5 × BWpass
   Fo = sqrt((Fcenter − 0.5 × BWpass) × (Fcenter + 0.5 × BWpass))
3. The following example demonstrates interpretation of simulation results with this component. From the user-specified poles/zeros, we derive:
   S21_Lowpass_Prototype= Gain*[(s-Z1)*...*(s-Zn)]/[(s-P1)*...(s-Pm)]
   We then check to see if S21_Lowpass_Protope is > 1. If yes, we scale S21 by a another factor to make sure S21_Max ≤ 1 . We then derive S11 (S22) from the following formula:
   S11² + S21² = 1
   In this example, when Gain is set > 0.471151, then S11 is derived as what you will expect. If Gain in your example is < 0.471151, then S11 derived from the preceding equation, will be much higher that what you will expect. In this situation, set Gain to be 0.1 so that S21 has a lot of insertion loss. But we assumed there is no insertion loss in deriving S11.
   There are other alternatives:
   • Use S2P_Eqn so that you can define the S21 and S11 polynomials however you want. You can define this as follows:
     s=j ω , S21=Gain*(s-Z1)*...*(s-Zn)/(s-P1)*...*(s-Pn), S11=<your choice>
   • Use BPF_Pole_Zero to model a lossless BPF, then use an attenuator to add insertion loss.