BPF_PoleZero (Bandpass Filter, Pole Zero)
Symbol
Available in ADS and RFDE
Parameters
Name |
Description |
Units |
Default |
---|---|---|---|
Numerator |
List of numerator coefficients |
None |
list(1) |
Denominator |
List of denominator coefficients |
None |
list(1,1.4,1) |
Gain |
Gain factor |
None |
1.0 |
Fcenter |
Passband edge frequency |
GHz |
1 |
BWpass |
Passband edge-to-edge width |
GHz |
1.0 |
StopType |
Stopband input impedance type: OPEN or SHORT |
None |
open |
Z1 |
Input port reference impedance |
Ohm |
50 |
Z2 |
Output port reference impedance |
Ohm |
50 |
Notes/Equations
- This is an S-domain filter.
- 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)) - 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:
S11^{2} + S21^{2} = 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.
- Use S2P_Eqn so that you can define the S21 and S11 polynomials however you want. You can define this as follows: