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# BPF PoleZero (Bandpass Filter, Pole Zero)

## BPF_PoleZero (Bandpass Filter, Pole Zero)

##### 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
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/Fo − Fo /Freq)/(Fhigh/Fo − Fo /Fhigh )
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_Max1 . 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.
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