Matching Pi Attenuator Calculator

Calculates the resistor values, attenuation, minimum attenuation, 'impedance', reflection coefficient, VSWR and return loss of a matching Pi attenuator. This can be built into a FLEXI-BOX and a transmission line (50 Ohm track) PCB is available which easily adapts for this circuit with one simple trimming operation. There is also a selection of 50 Ohm RF connectors available.

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The required input and output impedance are used to calculate the minimum attenuation possible for correct impedance matching with an equation from RF Design Guide, Systems, Circuits and Equations by Peter Vizmuller Published by Artech House ISBN 0-89006-754-6

Peter Vizmuller also gives equations for calculating the resistor values directly. This calculator uses equations that I have derived and first finds the output voltage with a source EMF of 2 Volts and therefore an input PD of 1 Volt. This calculation only applies to a matched circuit and a warning is given if matching cannot be achieved within the input constraints.

The traditional way of calculating attenuator values is using Voltage and Resistance as above but this calculator also includes Impedance Mismatch, which is rarely taken into account in attenuator calculators. As the real mechanism for Reflection at an Impedance Mismatch is that some electrons are reflected but there is no voltage change, it is more realistic to calculate using Current and Resistance. The results by calculating using Voltage or Current are identical which allows the possibilities that the change could be in voltage only or in Current only. It is easy to imagine the charged electrons taking different paths but an instantaneous change of charge is much more difficult to explain.

The following simple equations show how Resistance and Current are used to find the Input Power and Output Power in order to find the Attenuation. A simple input to output Current or Voltage ratio would not suffice as there is a change in Impedance.

Ohms Equation 6.

The EMF is again set at 2 Volts and the Incident Current is found by using Ohms Law.

Amps Equation 7.

The Incident Power to the attenuator is calculated using I² x R.

Watts Equation 8.

The Input Reflection Coefficient is calculated and this may have a negative value, indicating that there is a phase reversal of the Reflected current (and that the Characteristic Impedance of the source is higher than the Input Impedance of the attenuator). This negative sign is ignored for calculation purposes.

Equation 9.

The forward current into the attenuator is calculated using the Incident Current and the Reflection Coefficient if Mismatch Losses are selected in the calculator.

Amps Equation 10.

The current into the Series resistor is found using a current divider as described at https://engineering.usu.edu/students/tutoring/topics/electric-circuits/voltage-and-current-divider-circuits

Amps Equation 11.

The current divider is used again to calculate the Output Current from the Attenuator into the output load impedance Z₀.

Amps Equation 12.

The output current and output load impedance are used to calculate the output power.

Watts Equation 13.

The input power and output power are used to calculate the attenuation in the forward direction.

dB Equation 14.

Calculations are then repeated to find the reverse direction characteristics.

This calculator is provided free by Chemandy Electronics in order to promote the FLEXI-BOX

	INPUT DATA

Input Impedance:	Ohms
Output Impedance:	Ohms
Attenuation:	dB

	IDEAL VALUES

Ideal Shunt In resistor:	Ohms
Ideal Shunt Out resistor:	Ohms
Ideal Series resistor:	Ohms
Minimum attenuation to achieve impedance match:	dB

	SELECTED VALUES

Shunt In resistor:	Ohms
Shunt Out resistor:	Ohms
Series resistor:	Ohms
Mismatch Losses:	Included
(see note below)

	PARAMETERS

Forward Attenuation:	dB
Input Impedance:	Ohms
Input VSWR:
Input Reflection Coefficient:
Input Return Loss:	dB

Reverse Attenuation:	dB
Output Impedance:	Ohms
Output VSWR:
Output Reflection Coefficient:
Output Return Loss:	dB