![[diode pump circuit]](../../images/standing-waves-1.gif)
When a sine wave is passed into a transmission line, it's behavior 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. Some tutors use analogies in order to explain the principles and these often make it even more confusing. This study uses measurements of the constant sine waves and the resultant complex waveforms in a coaxial cable. The results of these measurements are processed with simple formulas and then 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 the student an understanding of what is really happening to the original sine wave and at the same time develop their skills with the mathematics and measurement techniques that are used every day in radio frequency technology.
A signal generator and a DVM are required plus the following test aids that we have developed specifically for the measurements.
1) Voltage and Current detector.
2) RF Bridge
The first one that is used and probably the one that needs most explanation is the Voltage and Current detector.
A sine wave can be detected by a diode pump circuit as in Figure 1.1. If there is a signal input to the anode of the diode of 1.4 Volts peak (1 Volt rms) and the diode is a Schottky with a forward voltage drop of 0.2 Volts, then the DC level on the diode cathode will be 1.2 Volts. If a digital voltmeter is now connected to the output of the circuit and the potentiometer is adjusted to give a meter reading of 1 Volt. The dc output of 1.0 Volts now indicated by the meter, represents the rms voltage present at the anode of the diode.
Figure 1.1
This circuit functions well, as long as there is an adequate input voltage to the diode. When the input voltage to the diode anode nears the voltage drop of the diode the output voltage drops disproportionately and the circuit becomes non-linear. There are methods of forward biasing the diode in order to reduce these errors but it was considered more suitable to reduce the errors mathematically.
Measurements are made at known voltage levels and the results are used to plot a curve. A formula is then fitted to the curve in order to find the constants for the diode in use. During our measurements, we will use a signal generator as the RF source and a DVM to monitor dc voltages. Most modern RF signal generators are 50 Ohms and indicate their output level in dBm, although some can indicate in Volts. DVM's indicate in volts and diode data is normally presented in Volts. We will therefore, use Volts as the common units.
If it is necessary to convert the signal generator output from dBm to Volts, we start by finding the voltage at the reference level of 0 dBm:
0 dBm = 1 mW into 50 Ohms
From Ohms law W = V2 / R
Change to Impedance V2 = W x Z
Substitute reference level Vref = (Wref x Z)^0.5 Formula 1.1
To find the voltage at a particular output power level:
From db = 20 x Log (V1/V2)
V1 = Alog(dB/20) x V2
Substitute required voltages Vout = ALog(dB/20) x Vref
Substituting Formula 1.1 for Vref Vout = ALog(dB/20) x (Wref x Z)^0.5 Formula 1.2
As an example, calculate the output voltage at +13 dBm:
V = ALog(13/20) x (0.001 x 50)^0.5
V = 4.467 x 0.2236 = 0.9988 Volts rms
We can now use Formula 1.2 (or the indicated signal generator output voltage) in a spreadsheet to give a range of signal generator output voltages related to one dB steps from - 10 dBm to +13 dBm. The generator output level in dB is placed in ascending order in the first column (A). The calculation and its result is placed in the second column (B). This has been done for you in Spreadsheet-01.xls, but it is better experience if you generate your own spreadsheets.
The Voltage and Current Detector is connected directly to the output of the Signal Generator, or with an adaptor and is terminated with a 50 Ohm load as shown in Figure 1.2. The Signal Generator output is set to +13 dBm (or 1 Volt rms) at a frequency of 50 MHz. The DVM is connected to the Voltage and Current Detector, voltage output and should indicate approximately 1 Volt.
Figure 1.2
![[test set up]](../../images/standing-waves-2.gif)
Technical Article Index <1 2 3> Page Number