# Understanding RF Transmission Lines by Measurement and Calculation

1.1) Introduction

When a sine wave is passed into a transmission line, it's behaviour is dependent on the conditions that it meets. The results can be complex and difficult to understand. Classical transmission line theory uses advanced mathematics and explanations that are not always logical, such as the theory of 'standing waves'. Some tutors use analogies in order to explain the principles and these are often incorrectly applied and can convince the student that the behaviour of the transmission line is different to reality. This study uses measurements of constant sine waves and the actual voltages and currents that are present in a coaxial cable. The results of these measurements are processed with simple formulas and then eventually made into charts with the aid of a spreadsheet, so that this visual data can be related to the, more mathematical, classical transmission line theory. The aim of the study is to give you an understanding of what is really happening to the original sine wave and at the same time develop your skills with the mathematics and measurement techniques that are used every day in radio frequency technology. By making the measurements and seeing the results you will have sound knowledge of the behaviour of a transmission line and not be confused by any contradictory statements in old text books, 'standing wave theory' or incorrect analogies.

The measurements start extremely simply and prove that the behaviour of the test equipment as you go along. This simple start ensures that the whole explanation is built on basic accepted fundamentals such as Ohms Law. Further measurements are then made in a sequence that gradually builds explanations of the transmission line behaviour on the facts that have already been established.

If you wish to perform the actual measurements, a signal generator and a digital multimeter (DMM) are required, plus the following test aids that we have developed specifically for these measurements. Explanations of the test aids can be found in the appropriate appendix and these should be studied carefully if you wish to substitute them with anything else.

The Voltage and Current Detector is connected to the output of the Signal Generator and is terminated with a 50 Ohm load as shown in Figure 1.1. The Signal Generator output is set to +13 dBm (or 1 Volt rms) at a frequency of 50 MHz. The DMM is connected to the Voltage and Current Detector, voltage output sockets and should indicate approximately 1 Volt dc. This shows how the Voltage and Current detector converts a 1 Volt rms high frequency signal into 1 Volt dc.

Figure 1.1 The Voltage and Current Detector remains connected to the output of the Signal Generator and is still terminated with a 50 Ohm load as shown in Figure 1.1. With the Signal Generator output still set to +13 dBm (or 1 Volt rms) at a frequency of 50 MHz. The DMM is connected to the Voltage and Current Detector, current output sockets and should indicate approximately 200 mV dc. This voltage represents the current that passes through the Voltage and Current detector and into the 50 Ohm load. This shows how the Voltage and Current detector converts a 20 mA high frequency signal into 200 mV Volt dc. The DMM is simply read as 200/10 = 20 mA.

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