The input impedance of the line depends on features like the ohmic resistance, the conductance, the inductance and the capacitance. It is also related to the resistance that loads the line at the opposite end and to both the frequency and the frequency and the voltage of the input signal.

The purpose of the first part of the test is to measure the modulus of the input impedance of the line under different load conditions: open line, line terminated on a matched load, short-circuited line. In the second part of the test we will measure the phase displacement between the input voltage and current, under the same conditions of line operation.

When the modulus and the phase displacement are known, the Impedance vector is fully identified.

Required components, instruments and accessories

Cable with intermediate sockets
Line termination resistors
Function generator
Oscilloscope

F10-5 shows the connections to be realized to perform the measurement of the input impedance modulus.

The signal generator with the line matching resistance supplies the transmission line at one end. The load at the opposite end is composed either by an infinite value resistance (open line), a matched load (68 ohms) or a null resistance (short-circuited line).

The resistance Rm with 1 ohm value in series connected between the generator and the transmission line allows to measure the value of the input current of the line for each value of the voltage connected t the line.

It is suggested that the measurements are repeated in more points within the frequency range 10 kHz to 1 MHz. Moreover, during each measurement the amplitude value of the input signal should be kept constant and of significant amplitude (for instance 10 V rms). This allows a comfortable measurement of the voltage drop value across Rs, which is necessarily small.

The results, gathered in tabular form, are subsequently processed calculating the modulus of the input impedance according to the following formula:

|Zin| = (Vin/I) = (Vin/Vm) . 1 Ω

The measurements have to be repeated in the three cases of open line, short-circuited line and closed on matches load.

The second part of the test consists in measuring the phase displacement between the current and the voltage at the input of the line, under the different load conditions stated above and for different frequency values.

It is possible to use either the measuring setup shown in F10-6 or the arrangement shown in the next F10-7, which allows to obtain the same measuring result with two different methods.

With the first method the duel-trace oscilloscope is connected with both channels for displaying the voltage waveform and the current waveform at the input of the line, respectively.

By using as trigger the input voltage signal, the phase displacement of the current against this signal can be evaluated by measuring the time delay after which the corresponding waveform is displayed against the former one.

With the second measuring method, the oscilloscope is connected with the X-axis to the input voltage signal and with the Y-axis to the current. On the screen the so-called Lissajous display is then determined, which allows the phase displacement between the two signals to be evaluated through the ratio of the semi-axis of the ellipse.

Again the results, gathered in a table, are subsequently translated into graphical form. This provides, together with the graph relevant to the input impedance modulus, the full information of modulus and phase of the input signal for different frequencies and for different load conditions of the line.