Model LC lowpass pi network

Ladder Filters sublibrary of the Physical library

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

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

The LC Lowpass Pi block then cascades the ABCD-parameters for
each circuit element 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 reference page for information about determining the modeling frequencies.

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

[L_{1}, L_{2}, ...]
is the value of the `'L'`

property, and [C_{1},
C_{2}, C_{3}, ...] is the
value of the `'C'`

property.

**Inductance (H)**Vector containing the inductances, in order from source to load, of all inductors in the network. All values must be strictly positive. The vector cannot be empty.

**Capacitance (F)**Vector containing the capacitances, in order from source to load, of all capacitors in the network. The capacitance vector must contain at least two elements. Its length must be equal to or one greater than the length of the vector you provide in the

**Inductance**parameter. All values must be strictly positive.

For information about plotting, see Create Plots.

See the LC Bandpass Pi block for an example of an LC filter.

[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.

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