Andy Collinson

Input Impedance
Meter Method
From the AC impedance triangle, the input or output impedance of a two terminal network can be determined by measuring the small signal AC currents and voltages. For the input, the voltage is measured across the input terminals and the current measured by inserting the meter in series with the signal generator. Use a fixed frequency say 1kHz and set the generator level to around 20 mV RMS. For example, if you read 20mV RMS and 10uA for current, then the impedance is 2k. With high impedance circuits, the current will become very small and difficult to measure, so an alternative method is called for.
An easy way to measure small input currents,is to use a fixed resistor, as in the diagram above. Measure the AC voltage at points V1 and V2, then the input current, Iin becomes:

Iin =	V2 - V1
	R1

The input impedance of the circuit under test is then found by:

Z =	V1
	Iin

Example
If you use a 10k resistor for R1 and measure V2=10.1mv and V1=10mV then :

Iin =	10.1mV - 10mV	=	0.1mV	= 10nA
	10k		10k

A current of 10nA would be very difficult to measure as the resolution of a digital meter would be very low, however measuring values of 10mV and 10.1mV is possible and allows the input impedance to be found:

Using a Simulation Program
To measure the input impedance over a complete spectrum of frequencies, use the following circuit:

The input is a constant current source, its value set to 1 amp. As the current sources in most simulation programs are perfect and have an infinite output impedance, you will have to use a high value resistor in parallel, as shown, to avoid simulation errors. As V= I * Z , and using 1 amp as shown for the current source, hence V=1*Z or V=Z. Hence measuring input voltage returns input impedance. The y-axis on the output graph may be labeled accordingly. See this example.
Output Impedance
Meter Method
Output impedance may also be determined using a similar technique. A fixed load resistor is used and the output voltage is measured first with full load, then without the load.

In the diagram above, Zo is the internal output impedance of the network to be measured. The term network is a general term, as the circuit could be anything, an amplifier, filter, oscillator, etc. The network is drawn as a Thevenin source.

To find the output impedance the output voltage is measured first with no load resistor, then with a fixed load (purely resistive).

First, the load resistor RL is removed and output voltage (V) measured and recorded. Then RL is placed back in circuit and the output voltage under load (V_L). The output impedance, Zo is now found by Ohm's Law for AC circuits. As the load is purely resistive Z=V/I, where "V" is voltage drop across the output impedance: ( V - V_L ), and "I" the output current, V_L/RL. Thus:

Zo =	( V-VL )
	VL/RL

or re-arranging:

Zo =	RL ( V-VL )
	VL

Using a Simulation Program
To measure the input impedance over a complete spectrum of frequencies, use the following circuit:

The input is a constant current source, its value set to 1amp. As the current sources in most simulation programs are perfect and have an infinite output impedance, you will have to use a high value resistor in parallel, as shown, to avoid simulation errors. As V= I * Z , and using 1 amp as shown for the current source, hence V=1*Z or V=Z. Hence measuring output voltage returns output impedance. The y-axis on the output graph may be labeled accordingly.