J.K.U.A.T

Bsc. Electrical and Electronics Engineering

MICROWAVES LABORATORY REPORT

MEASUREMENT OF VOLTAGE STANDING WAVE RATIO23rdDecember 2011

MICROWAVES

Mwai Dan T.EN271-0329/2007

MEASUREMENT OF VOLTAGE STANDING WAVE RATIO

OBJECTIVES1. To be able to explain the meaning of Voltage Standing Wave Ratio.2. To know two Methods of measuring VWSR and when to use them.

EQUIPMENT

THEORYThe electromagnetic field at any point of a transmission line (such as a waveguide) can be considered as the sum of two travelling waves, one travelling in each direction. When a continuous wave (the ‘incident wave’) reaches a discontinuity in the transmission line, a portion of it (the ‘reflected wave’) is reflected back down the line. Usually we are trying to send R.F. power from some source to a load.

Consequently, any power that is reflected cannot enter the load. Often, therefore, we try to avoid reflections. When reflection does occur, the incident and reflected waves will reinforce each other in some places, and in others they will tend to cancel each other out. The stationary pattern of larger and smaller amplitudes is called a ‘standing wave’. The ratio between the largest and smallest amplitudes is called the ‘standing wave ratio’. Usually the voltage amplitude is the one considered, so that the Voltage Standing Wave Ratio (VSWR) is defined as:

VSWR =

If there is no reflection, the VSWR becomes 1.

QUANTITY IDENTIFICATION LETTER

DESCRIPTION

1 Control Console

2 A Variable Attenuator

1 B Slotted-line

1 P X-Band Oscillator

1 R Short-circuit Terminator

1 S Probe Detector Assembly

Fig 2.1

Fig 2.1 above shows at (a) a signal source and load connected by a transmission line. If the load is not exactly matched to the line, the standing wave pattern shown at (b) is produced.

The instrument most commonly used to measure VSWR is a slotted length of waveguide section in which the electric field can be sampled by a movable probe.

Fig 2.2

Fig 2.2(a) above shows the construction. A small probe, connected to a diode detector, extends through the slot in the waveguide wall to sample the voltage on the line. The probe and detector are mounted on a carriage which can be moved along to sample the voltage at different points along the line.

If the slotted line matches the remainder of the line, it can be inserted without introducing further reflections. Suppose that it extends between A and B in fig 2.1. Then emax and emin can be measured at points X and Y respectively. Absolute measurements are not required, but only a ratio.

Most microwave detectors, including the diode detector, have a square-law characteristic, , where

is output D.C. current, is the R.F. voltage on the line and is a constant introduced by the detector and

the probe coupling. What is actually measured therefore is the ratio of maximum to minimum current, from which the VSWR is obtained as follows:

The preceding method is perhaps the simplest one, and is often referred to as the ‘direct’ method. It is

satisfactory so long as accurate measurements of the relative values of and can be made. But when

becomes very large the detector can no longer be relied on to have a predictable characteristic.

On the other hand if is very small, the probe may have to penetrate so far into the field to get a

measurable reading, that the field is distorted, changing the VSWR. Consequently for values of VSWR greater than about ten, the ‘double minimum’ method is usually employed.

Fig. 2.3: Double minimum method

The principle is illustrated in fig 2.3, in which the detector output(proportional to field strength squared) is plotted against position. The probe is moved along the line to find the minimum value of signal. It is then moved either side to determine two positions at which twice as much detector signal is obtained. The distance d between these two positions then gives the VSWR according to the formula:

Another way of overcoming the problem of a large VSWR is to use a calibrated attenuator. The minimum signal is measured with a minimum value of attenuation. The maximum value is then found, and sufficient attenuation is introduced to reduce the detector reading to the same value as before. The VSWR is then simply the volt ratio corresponding to the change of attenuation. Thus if the attenuator is calibrated in dB,

= 10 log10

PROCEDURE1. The apparatus was connected as shown below.

2. On the control console, the supply to the oscillator was switched on and its left-hand switch for internal keying was set. The meter was switched to read the detector output.

3. The right hand load attenuator was set to minimum attenuation (vane fully outside the waveguide). The sensitivity control was set to maximum. Starting with the attenuator (source end) at about 20o from 0 (maximum attenuation).

4. The source Attenuator was adjusted so that the maximum reading of the meter was about full scale. The source Attenuator was now set outside the range 200 to 600 open. Its locknut was slackened and screwed in until a satisfactory reading was obtained

5. Standing Wave Pattern (large VSWR)

The Detector was slid along its slot. Sharp drops (minima) in the meter reading were observed. The maximum and minimum meter readings were recorded in the table headed ‘Large VSWR’ and the scale position at which they occurred, a graph of meter reading against position was plotted.

6. Standing Wave Pattern (small VSWR)

The load Attenuator was set for maximum attenuation (vane fully in). Without making any other adjustments, the experiment was repeated, recording the results in a further table headed ‘Low VSWR’. Some variation of the meter reading was seen. On the same axis as before the resulting

graph was plotted labeling the two graphs to distinguish them.

The VSWR is the ratio between the maximum and minimum values of field strength. Since the Detector operates on a square law, the VSWR can be calculated as

This calculation was made for the small VSWR experiment.

The source attenuator was set to approximately 20o. The detector was moved to find a minimum. The detector position was carefully adjusted to find the true minimum meter reading. The minimum reading was recorded. The detector was moved carefully to the left until the meter reading was double the minimum value. This position was recorded on the scale. The detector was moved past the minimum position to the right and again the position where the meter reading was double the minimum value was found. The distance between the two positions gave the twice minimum reading.

RESULTS

Large VSWR Meter reading Distancemaximum Minimum Maximum Minimum5mA 0 2.4cm 1.5cm5mA 0 4.2cm 3.3cm5mA 0 5.9cm 5.1cm

Small VSWR Meter reading Distancemaximum Minimum Maximum Minimum0.75 0.4 3.0cm 2.5cm0.75 0.35 5.0cm 4.1cm0.7 0.4 6.65cm 5.95cm

Double minimum methodMeter reading Distance0.2mA 3.7cm0.4mA 4.2cm0.4mA 3.3cm

CALCULATIONS

VSWR

VSWR=

For the Large VSWR this gives a value of infinity. The direct method becomes unreliable.

For the small VSWR various values were obtained as 1.875, 2.14 and 1.75 the average of which becomes 1.9

For the double minimum method

Where

g= 36mm,

= 0.2778

VSWR= =3.78

DISCUSSIONWhen the load is matched to the transmission line the reflection coefficient is zero and the magnitude of voltage along the line is constant. Such a line is sometimes said to be flat. When the load is mismatched however, the presence of a reflected wave leads to standing waves where the magnitude of the voltage on the line is not constant.

The maximum value is given by

= (1+

The minimum value is given by

= (1-Г) where Г is the reflection coefficient.

As Г increases the ratio of to increases, so a measure of the mismatch of the line, called the

VSWR is given by

VSWR=

A VSWR of 1 implies a matched load.

Thus if the end of a wave guide does not absorb the incident energy a standing wave is set up which is a stationary pattern of field intensity which repeats cyclically as a detector moves a lot the transmission path. The ratio

is known as the VSWR. When it is small (near 1) it can be measured directly. Because normal detectors produce an output proportion to the square of the field intensity, the square root of the ratio of detector output is taken.

For large values of VSWR direct measurement of ratio becomes impractical and the double minimum method is then useful.

Standing wave pattern in a wave guide are formed when reflections occur in a waveguide. This causes the incident and reflected wave to cancel each other out in some places and reinforce each other in other places. Reflections are undesirable because the wave guide is meant to deliver R.F. power from some source to a load. Therefore, they should be avoided.

Both direct method and double minimum methods were used in obtaining VSWR. The direct method is simple and satisfactory so long as accurate measurements of the relative values of emax and emin can be made. But when emax becomes very large the detector can no longer be relied on to have a predictable characteristic. Also when emin is very small, the probe may have to penetrate so far into the field to get measureable reading, distorting the field and changing VSWR. Using this method, the value of VSWR was obtained to be 1.9. Double minimum method is suitable for measuring large values of VSWR. When double minimum method was used, guide wavelength was found to be 36mm. VSWR was found to be 3.78.

For large VSWR, sharp drops in the meter reading were observed when the detector was slid along its slot. The reason is that there was nothing to absorb incident energy, and so nearly all of it was reflected back. The reflected wave cancelled out the incident wave at places where their phases were opposite.

For low VSWR, a little variation of the meter reading from that of large VSWR was observed. The load attenuator absorbed most of the energy travelling towards the end of the transmission line, and if the remainder got reflected from the end, the attenuator absorbed most of that.

Schematic of a slotted line measurement with short circuit termination

The slotted-line measurement was effected by cutting a non-radiating slot along the direction of propagation in a coaxial or waveguide transmission line and sliding a rectifying detector diode along the slot to sample the rectified time-average voltage amplitude as a function of position along the line. This fixture was called a slotted line. The ratio of the maximum to minimum voltage values is the voltage standing-wave ratio, or VSWR. The VSWR coupled with the location of the associated voltage minimum (null) could be used to determine the load impedance ZL.

First a short circuit is connected at the end of the transmission line prior to connecting the load and the positions of the resulting voltage minima, or nulls, recorded. These null locations are equivalent to the electrical position of the load plane. The rectified voltage amplitude varies sharply with position near a null, yielding the most precise measurement of the equivalent load positions. The distance between two successive minima is one-half wavelength at the operating frequency, providing a means of determining the actual operating frequency of the generator. Each set of VSWR and null data is taken at a single microwave frequency. To obtain data for a band of frequencies, the measurement must be re-performed at each frequency of evaluation.

SUMMARYIn this assignment it was seen that:

If the end (or other discontinuity) of a waveguide does not absorb the incident energy, a standing wave is set up, which is a static pattern of field intensity which repeats cyclically as a detector moves along the transmission path.

The ratio, maximum Intensity is known as the VSWR. . minimum intensity

When it is small (near 1), it can be measured directly because normal detectors produce an output proportional to the square field intensity, the square root of the ratio of detector output is taken.

For large values of VSWR, direct measurement of the ratio becomes impracticable. The double-minimum method is then used.

Sources for errors may include parallax while taking the measurement readings.

REFERENCES1. Laboratory manual provided.2. Electromagnetic Waves and Antennas by Sophocles J. Orfanidis, Rutgers University.