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# LC Bandpass Pi

Model LC bandpass pi network

## Library

Ladder Filters sublibrary of the Physical library

## Description

The LC Bandpass Pi block models the LC bandpass pi network described in the block dialog box, in terms of its frequency-dependent S-parameters.

For each inductor and capacitor pair in the network, the block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. For each series pair, A = 1, B = Z, C = 0, and D = 1, where Z is the impedance of the series pair. For each shunt pair, A = 1, B = 0, C = Y, and D = 1, where Y is the admittance of the shunt pair.

The LC Bandpass Pi block then cascades the ABCD-parameters for each series and shunt pair at each of the modeling frequencies, and converts the cascaded parameters to S-parameters using the RF Toolbox™ abcd2s function.

See the Output Port block for information about determining the modeling frequencies.

The LC bandpass pi network object is a two-port network as shown in the following circuit diagram.

[L1, L2, L3, L4, ...] is the value of the 'L' property, and [C1, C2, C3, C4, ...] is the value of the 'C' property.

## Dialog Box

### Main Tab

Inductance (H)

Vector containing the inductances, in order from source to load, of all inductors in the network. The inductance vector must contain at least three elements. All values must be strictly positive.

Capacitance (F)

Vector containing the capacitances, in order from source to load, of all capacitors in the network. Its length must be equal to the length of the vector you provide in the Inductance parameter. All values must be strictly positive.

### Visualization Tab

For information about plotting, see Create Plots.

## Examples

### Using a Ladder Filter Block to Filter Gaussian Noise

This example provides complex random noise in Gaussian form as input to an LC Bandpass Pi block. A DSP System Toolbox™ Spectrum Scope block plots the filtered output.

The DSP System Toolbox Random Source block produces frame-based output at 512 samples per frame. Its Sample time parameter is set to 1.0e-9. This sample time must match the sample time for the physical part of the model, which you provide in the Input Port block diagram.

The Input Port block specifies Finite impulse response filter length as 256, Center frequency as 700.0e6 Hz, Sample time as 1.0e-9, and Source impedance as 50 ohms.

The LC Bandpass Pi block provides the inductances for three inductors, in order from source to load, [1.4446e-9, 4.3949e-8, 1.4446e-9]. Similarly, it provides the capacitances for three capacitors [3.5785e-11, 1.1762e-12, 3.5785e-11].

The following plot shows a sample of the baseband-equivalent RF signal generated by this LC Bandpass Pi block. Zero (0) on the frequency axis corresponds to the center frequency specified in the Input Port block. The bandwidth of the frequency spectrum is 1/sample time. You specify the Sample time parameter in the Input Port block.

The Axis Properties of the Spectrum Scope block have been adjusted to show the frequencies above and below the carrier. The Minimum Y-limit parameter is -90, and Maximum Y-limit is 0.

## References

[1] Ludwig, Reinhold and Pavel Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000.

[2] Zverev, Anatol I., Handbook of Filter Synthesis, John Wiley & Sons, 1967.