Understanding RF Transmission Lines by Measurement and Calculation page 8

5.5) Relative Phase of REFLECTED Voltages from an OPEN and a SHORT

We can now compare the phases produced by measuring voltages from OPEN and SHORT terminations.

Phase at an OPEN

In paragraph 5.2, with an OPEN at the end of the cable, the V/C Detector indicated a voltage null at a quarter wave from the OPEN. As both the very small INCIDENT and REFLECTED currents that passed through the voltmeter in the same direction, the currents were summed. Therefore a null result indicates that the INCIDENT and REFLECTED currents passing through the voltmeter were 180° out of phase. As the phase shift in the cable in one direction was 90° giving a total phase shift in the cable for both directions of 180°, then there was no phase shift at the OPEN. The behaviour of the OPEN is as though the signal goes all of the way to the end of the OPEN and then simply reflects with no phase change.

Phase at a SHORT

In paragraph 5.4, with a SHORT at the end of the cable, the V/C Detector indicated a voltage sum at a quarter wave from the SHORT. Both the small INCIDENT and REFLECTED currents passed through the voltmeter in the same direction, and the currents were summed. Therefore a result of double the source voltage indicates that the INCIDENT and REFLECTED voltages were in phase. As the phase shift in the cable in one direction was 90° giving a total phase shift in the cable for both directions of 180°, then the total 'round trip' phase shift at the SHORT was 180°.

Relative phases

It can now be simply deduced that the voltage phase shift with a SHORT is 180° and the voltage phase shift with an OPEN is 0°, giving 180° difference. These relative phases can be observed on a Vector Network Analyser and most experienced VNA users will be familiar with this. With a Smith chart giving a dot on the right hand of the display for an OPEN and a dot on the left hand of the display for a SHORT.

5.6) Relative Phase of INCIDENT and REFLECTED Currents from a SHORT

With the test equipment set up as in Figure 5.1, the DMM is transferred to the current output of the Voltage and Current Detector.

The Signal Generator is again set to give an output of +0 dBm at a frequency of 37.5 MHz as calculated for the 2 m cable in paragraph 5.2. This gives an amplifier output of approximately +15 dBm (1.26 Volt rms. at 0.025 Amps into 50 Ohms). The SHORT Termination is now connected to the output of the Two Metre Cable.

While observing the DMM, the Signal Generator frequency is slowly reduced until a current null is reached. The frequency of the Signal Generator will return to virtually the same frequency as previously recorded for a voltage null into an OPEN in paragraph 5.2.

Figure 5.4 shows how the currents (If and Ir) flowing through the current transformer of the Voltage and Current Detector flow in opposite directions, which causes the currents to fundamentally subtract. It can be seen from the Figure 5.4 that there is a 90° phase shift along the cable in the INCIDENT direction plus 90° at the SHORT, followed by 90° in the SHORT in the REFLECTED direction plus another 90° along the cable giving a total of 360° of phase shift Thus the INCIDENT and REFLECTED signals have the same phase at the current transformer. As the two currents are in phase at the transformer and the transformer subtracts, the final result is a cancellation and the DMM reads a null current.

Figure 5.4

[Diagram of current flow in coaxial cable and current transformer]

 

5.7) Relative Phase of INCIDENT and REFLECTED Currents from an OPEN

With the test set up still as above and the signal generator frequency still set as in paragraph 5.6, an OPEN is selected on the Termination Box. The DMM now indicates a current of approximately 0.05 Amps because the INCIDENT and REFLECTED currents now sum. The two signals are 180° out of phase at the current transformer because there is no phase change at an OPEN but flow in opposite directions, and the two negatives make a positive giving a sum. In fact, the peak current vector difference is being indicated.

Figure 5.2

[Diagram of current flow in coaxial cable and current transformer]

 

5.8) Relative Phase of REFLECTED Currents from an OPEN and a SHORT

We can now compare the phases produced by measuring currents from OPEN and SHORT terminations.

Phase at a SHORT

In paragraph 5.6, with a SHORT at the end of the cable, the V/C Detector indicated a current null at a quarter wave from the SHORT. As the INCIDENT and REFLECTED currents that passed through the transformer were in opposite direction, the currents were basically subtracted. Therefore a null result indicates that the INCIDENT and REFLECTED currents passing through the voltmeter were in phase. As the phase shift in the cable in one direction was 90° giving a total phase shift in the cable for both directions of 180°, then there was 180° phase shift at the SHORT.

Phase at an OPEN

In paragraph 5.7, with an OPEN at the end of the cable, the V/C Detector indicated a current sum at a quarter wave from the OPEN. As the INCIDENT and REFLECTED currents that passed through the transformer were in opposite direction, the currents were basically subtracted. Therefore a result of double the source current indicates that the INCIDENT and REFLECTED currents were 180° out of phase. As the phase shift in the cable in one direction was 90° giving a total phase shift in the cable for both directions of 180°, then there was no phase shift at the OPEN.

Relative phases

It can now be simply deduced that the current phase shift with a SHORT is 180° and the current phase shift with an OPEN is 0°. Exactly the same shift as that found for voltages in paragraph 5.5.

5.9) Relative Phases of Voltage and Current Into a Mismatch

Using the data collected in the proceeding measurements, it is possible to make further observations. If the voltage and current measurements into an OPEN at 90° are considered, it can be seen that the DMM indicates a voltage minimum and a current maximum. Conversely, if the voltage and current measurements into a SHORT at 90° are considered, it can be seen that the DMM indicates a voltage maximum and a current minimum. We have observed that this difference in readings between voltage and current is due to the fact that the voltage measurement is an addition and the current measurement is a subtraction. We can see from this that the voltage and current in any one direction are definitely in phase. In the classical study of transmission lines the indication of the meters that the voltage was at a maximum when the current was at a minimum (and vice versa), was taken to mean that the current and voltage were 180° out of phase, which is obviously not true.

The operation of the transmission line now makes sense. The signal passing along the line is formed of charged particles. The voltage and current from any charged particle is related to the amount of charge on that individual particle. This charge gives the particle an electric field and a magnetic field and they all travel together as an entity. The illogical concept that the voltage or the current can move independently of the particle is no longer required.

 

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