Understanding RF Transmission Lines by Measurement and Calculation page 7

5.3) INCIDENT Voltages in a Coaxial Cable

It was proven in 4.2 that the INCIDENT signal power level in a coaxial cable remains constant regardless of the impedance of the termination on the end of the cable. In this measurement it is demonstrated that the INCIDENT voltage remains constant regardless of the termination used. The INCIDENT input voltage into the cable is measured first, followed by a measurement of the output voltage. The results are used to calculate the sum input voltage which is then compared with the measured sum input voltage recorded in 5.2.

Measuring Input Voltage

The equipment is still connected as per Figure 5.1 and the signal generator frequency Fg is left set for a voltage null at the Voltage and Current Detector. (Ensure that the null {sum} voltage into the OPEN Termination is recorded as per paragraph 5.2). The OPEN Termination is now replaced by the LOAD Termination and so there is no reflected signal. The measured sum input voltage is therefore actually the INCIDENT input voltage. This input voltage to the coaxial cable is recorded and the result linearised.

Measuring Output Voltage

 The Voltage and Current Detector is now moved to the end of the Two Metre Cable and the LOAD Termination is fitted as in Figure 5.2

Figure 5.2

[Test set up for output voltage]

  The INCIDENT output voltage ( Vf ) of the coaxial cable is recorded and the result is linearised.

 The voltage drop for the return trip can now be calculated using Formula 5.4 and the reflected voltage found.

Reflected Voltage  ( Vr ) = Vout2 / VfFormula 5.6

   The INCIDENT voltage and reverse voltage are 180° out of phase, therefore the sum voltage is a simple subtraction.

Calculated Sum Input Voltage = Vf - Vr

The Calculated Sum Input Voltage can now be compared to the measured result obtained in 5.2 and it can be clearly seen that they are virtually the same. Thus demonstrating that the INCIDENT voltage remained constant at the input to the cable, even though the termination on the output was changed from OPEN to LOAD. It follows that if both the power and the voltage have remained constant, then the current must also have remained constant, because P = V x I. This measurement can be repeated using current measurements if further proof is required with If and I being measured . The termination is replaced by a SHORT for the sum input current measurement and the generator frequency remains unchanged. The results of the calculated sum current and the measured sum current are similar proof that the INCIDENT conditions remain unchanged by the termination at the end of the cable.

5.4) Relative Phase of INCIDENT and REFLECTED Voltages from a SHORT

With the test set up as in Figure 5.1 and the signal generator frequency still set as in paragraph 5.2, a SHORT is selected on the Termination Box. The DMM now indicates a sum voltage of approximately 2.52 Volts because the INCIDENT and REFLECTED voltages are in phase. It is now possible to use the data collected to logically deduce the phase relationship at the SHORT.

 It can be seen that the Voltage/Current Detector voltage output is the vector sum of the peak INCIDENT and REFLECTED voltages. The measured voltage is twice the peak voltage in one direction, therefore both signals are measured at their peak, and must therefore be in phase, with an overall180° phase shift in both the INCIDENT and REFLECTED directions as shown in Figure 5.3 below.

 

Figure 5.3

[Diagram of current flow in coaxial cable and voltmeter]

As the length of the cable has been established in paragraph 5.2 as 90° there must be a further 90° phase shift at the SHORT on the end of the cable, giving the total phase shift in one direction of 180°. The overall phase for the return trip then has to be 180° + 180° = 360°, thus making the INCIDENT and REFLECTED voltages in phase at the Voltage/Current Detector junction. Therefore, it can be concluded that a SHORT produces a total phase change of 180°.

Note: Detailed measurements made suggest that it is only the very last few degrees of the signal in a shorted transmission line that undergoes this 90° phase reversal in one direction and this part of the cable probably acts rather like an inductor but with a similar propagation delay time to the actual transmission line.

It is of course the same direction of the currents in the voltmeter circuit and their identical phases which causes the voltage summing. Although the voltmeter indicates 2.52 Volts it should be understood that this is a vector sum reading and that there is in reality two sources of 1.26 Volts at the junction of the voltmeter circuit and the coaxial cable. Both the INCIDENT and the REFLECTED signals obey the transmission coefficient formula (5.7) for a singular signal, because they are independent streams of charged particles. The particles are travelling in opposite directions, are not influenced by each other, have momentum and must therefore go somewhere. This causes them to behave within the rules of individual signals and their transmission coefficients are both as in formula 5.7.

[Formula for transmiaaion coefficient]Formula 5.7

It is only after the charged particles have entered the voltmeter circuit that they behave as a singular current. The voltmeter now has twice the current as that previously flowing for a simple INCIDENT voltage measurement in Para 4.2 when it indicated 1.26 Volts. The voltmeter has the same resistance as in Para 4.2 with twice the current and thus now indicates approximately 2.52 Volts. The voltmeter circuit behaves correctly to Ohms law for each individual current, IVf or IVr. The momentum of the two separate charged particle streams entering the voltmeter circuit has taken the overall complex performance (i.e. the forced adding of two individual currents) in the voltmeter circuit out of the scope of Ohms law, which does not allow for the dynamics of the complex situation and only covers the simple individual currents.

Formula 5.7 is from Transmission Line Design Handbook by Brian C Wadell, Artech House 1991 page 497 (C.3).

 

 

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