LC Lowpass Pi

Model LC lowpass pi network

• 

Libraries:
RF Blockset / Equivalent Baseband / Ladder Filters

Description

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.

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

Examples

Use Ladder Filter Block to Filter Gaussian Noise

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

• Open Script

Parameters

Main

Inductance (H) — Inductance of the LC Lowpass Pi

2.8318e-6 (default) | vector

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) — Capacitance of the LC Lowpass Pi

[5.3296e-9 5.3296e-9] (default) | vector

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

Source of frequency data — Frequency data source

User-specified (default)

Frequency data source, specified as User-specified.

Frequency data (Hz) — Frequency data range

[1:1.0e5:4e6] (default) | vector

Frequency data range, specified as a vector in hertz.

Reference impedance (ohms) — Reference impedance

50 (default) | nonnegative scalar

Reference impedance, specified as a nonnegative scalar in ohms.

Plot type — Type of data plot

X-Y plane (default) | Composite data | Polar plane | Z Smith chart | Y Smith chart | ZY Smith chart

Type of data plot to visualize using the given data, specified as one of the following:

• X-Y plane — Generate a Cartesian plot of the data versus frequency. To create linear, semilog, or log-log plots, set the Y-axis scale and X-axis scale accordingly.

• Composite data — Plot the composite data. For more information, see Create Plots Using Equivalent Baseband Library Blocks.

• Polar plane — Generate a polar plot of the data. The block plots only the range of data corresponding to the specified frequencies.

• Z smith chart, Y smith chart, and ZY smith chart — Generate a Smith^® chart. The block plots only the range of data corresponding to the specified frequencies.

Y parameter1 — Type of parameters to plot

S11 (default) | S12 | S21 | S22 | GroupDelay | OIP3 | NF | ...

Type of parameters to plot based on the Plot type you set, specified as one of the following.

Plot type	Y parameter1
X-Y plane	S11, S12, S21, S22, GroupDelay, OIP3, NF, NFactor, and NTemp.
Composite data	No Y parameter1 to set.
Polar plane	S11, S12, S21, and S22
Z Smith chart	S11 and S22.
Y Smith chart	S11 and S22.
ZY smith chart	S11 and S22.

Y parameter2 — Type of parameters to plot

S11 (default) | S12 | S21 | S22 | GroupDelay | OIP3 | NF | ...

Type of parameters to plot based on the Plot type you set, specified as one of the following.

Plot type	Y parameter2
X-Y plane	S11, S12, S21, S22, GroupDelay, OIP3, NF, NFactor, and NTemp.
Composite data	No Y parameter2 to set.
Polar plane	S11, S12, S21, and S22
Z Smith chart	S11 and S22.
Y Smith chart	S11 and S22.
ZY smith chart	S11 and S22.

Y format1 — Plot format

Magnitude (decibels) (default) | Mag | Magnitude (linear) | Angle | Real | Imaginary | ...

Plot format, specified as one of the following.

Y parameter1	Y format1
S11, S12, S21, and S22.	Magnitude (decibels), Magnitude (linear), Angle(degrees), Angle(radians), Real, and Imaginary.
GroupDelay	ns, us, ms, s, and ps.
OIP3	dB, dBm, W, and mW.
NF	Magnitude (decibels)
NFactor	None
NTemp	Kelvin

Dependencies

To enable Y format1, set Plot type to X-Y plane.

Y format2 — Plot format

Magnitude (decibels) (default) | Mag | Magnitude (linear) | Angle | Real | Imaginary | ...

Plot format, specified as one of the following.

Y parameter2	Y format2
S11, S12, S21, and S22.	Magnitude (decibels), Magnitude (linear), Angle(degrees), Angle(radians), Real, and Imaginary.
GroupDelay	ns, us, ms, s, and ps.
OIP3	dB, dBm, W, and mW.
NF	Magnitude (decibels)
NFactor	None
NTemp	Kelvin

Dependencies

To enable Y format2, set Plot type to X-Y plane.

X parameter — Frequency plot

Freq (default)

Frequency plot, specified as Freq.

X format — Frequency plot format

Hz (default) | Auto | kHz | MHz | GHz | THz

Frequency plot format, specified as one of the following.

Auto	Hz	kHz	MHz
GHz	THz

Y scale — Y-axis scale

Linear (default) | Log

Y-axis scale, specified as Linear or Log.

Dependencies

To enable this parameter, set Plot type to X-Y plane.

X scale — X-axis scale

Linear (default) | Log

X-axis scale, specified as Linear or Log.

Dependencies

To enable this parameter, set Plot type to X-Y plane.

Plot — Plot specified data

button

Plot the specified data using the plot button.

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.

Version History

Introduced in R2013a