# T & Pi Impedance Matching & Phase Shifting Networks

Author: R.J.Edwards G4FGQ © 13th January 1999This program simultaneously computes component values for both the T and Pi networks to match any two resistive terminations and having a specified value of phase shift between output and input terminals. For both T and Pi networks there are two versions - phase lagging and phase leading. Thus there are four networks displayed from which to select for the required purpose.

Frequency is normally entered in MHz, L is in units of micro-henrys and C in pico-farads. At very low frequencies computed data may be better displayed if frequency is entered in KHz. Measurement units will then be milli-henrys and nano-farads.

An important network characteristic is transmission loss. All four networks, whether T or Pi, phase-lag or phase lead, have identical losses provided all inductors have the same value of Q and capacitor losses are assumed to be negligible. For a given Q the program computes percent of input power lost in the network and its equivalent in decibels.

The overall loss and phase shift of a number of cascaded networks, matched at their junctions, is simply the sum of the individual dB losses and shifts.

Loss increases when the impedance transformation ratio of a network departs from unity and when phase shift approaches 180 degrees the loss is very large. For ratios exceeding 50 to 1, or when the required shift exceeds 120 degrees, overall loss can be reduced by cascading two or more networks.

T sections can be cascaded with Pi's provided common junction Z's are matched. Junction impedances may be selected to provide convenient L and C values, or to suit component RF voltage and current ratings.

T and Pi networks are often used to provide RF amplifiers with a particular value of load resistance. The useful bandwidth or selectivity of such networks is critical. When a narrow band is required a network behaves as a tank circuit with a large circulating current, a large phase delay, and unless high-Q coils coils are used loss will be high. Wideband networks having small phase delays have high loss only when input and output resistances are very dissimilar. Pi low-pass nets can incorporate amplifying-device output and input capacitances.

Other applications are phase controlling networks for insertion in beam antenna feed lines, artificial signal delay lines, and for high power pulse generation.

Bandwidth between approximate frequencies at which the response falls by 3 dB from that at the design frequency is computed together with circuit operating Q. Use key 'T' to toggle between the two sets of output data.

Run this Program from the Web or Download and Run
it from Your Computer

This program is self-contained and ready to use. It does not require
installation. Click this link TPiNet then
click *Open* to run from the web or *Save* to save the program
to your hard drive. If you save it to your hard drive, double-click the
file name from Windows Explorer *(Right-click Start then left-click Explore
to start Windows Explorer)* and it will run.

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