Slotted line
Slotted lines are used for
Slotted lines can measure standing waves, wavelength, and, with some calculation or plotting on Smith charts, a number of other parameters including reflection coefficient and electrical impedance. A precision variable attenuator is often incorporated in the test setup to improve accuracy. This is used to make level measurements, while the detector and VSWR meter are retained only to mark a reference point for the attenuator to be set to, thus eliminating entirely the detector and meter measurement errors. The parameter most commonly measured by a slotted line is SWR. This serves as a measure of the accuracy of the impedance match to the item under test. This is especially important for transmitting antennas and their feed lines; high standing wave ratio on a radio or TV antenna can distort the signal, increase transmission line loss and potentially damage components in the transmission path, possibly even the transmitter.
Slotted lines are no longer widely used, but can still be found in budget applications. Their main drawback is that they are labour-intensive to use and require calculation, tables, or plotting to make use of the results. They need to be made with mechanical precision and the probe and its detector need to be adjusted with care, but they can give very accurate results.
Description
The slotted line is one of the basic instruments used in
Slotted lines are relatively cheap
Operation
The slotted line works by sampling the
The disturbance to the field inside the line caused by the insertion of the probe is minimised as far as possible. There are two parts to this disturbance. The first part is due to the power the probe has extracted from the line and manifests as a
Test setup
A typical test setup with a waveguide slotted line is shown in figure 2. Referring to this figure, power from a test equipment source (not shown) enters the apparatus through the co-axial cable on the left and is converted to waveguide format by means of a
The probe is connected to a detector and a display meter (not shown in figure 2). These can be, respectively, a
Measurements
Measurements of microwave power can be made directly, usually with a thermistor based detector and meter. However, these instruments are expensive and a common meter used in measurements with a slotted line is instead a cheaper low-frequency VSWR meter. The microwave power source is
Maxima and minima
When the slotted line is terminated with a precision matching load there is no variation in the detected power along the line, other than a very small decrease due to losses in the line. However, when this is replaced by a
The extrema are not of any great interest in themselves, but are used in the calculation of several more useful parameters. Some of these parameters require the measurement of the exact position of the extremum. Either maxima or minima can equally be used, from a mathematical point of view, but minima are preferred because they are always much sharper than maxima, especially for large reflections, as shown in figure 4. Additionally, the probe causes less disturbance to the field near a minimum than it does near a maximum.[10]
Wavelength
Wavelength is determined by measuring the distance between two adjacent minima. This distance will be λ/2. There is no need for a DUT, better results are obtained with the reference short in position.[11]
Standing wave ratio
Standing wave ratio (SWR or VSWR) is a basic parameter and the one most commonly measured on a slotted line. This quantity is of particular importance for transmitter antennae. A high SWR indicates a poor match between the feed line and the antenna, which increases wasted power, can cause damage to components in the transmission path, possibly including the transmitter, and cause distortion to TV, FM stereo and digital signals. With the input power set so that the maxima are at 0 dBm, a measurement of a minimum in decibels will directly give SWR (after discarding the minus sign).[12]
Reflection coefficient
The reflection coefficient, ρ, is the ratio of the reflected wave to the incident wave. In general it is a complex number. The magnitude of the reflection coefficient can be calculated from the VSWR measurement by,
where VSWR is the standing wave ratio expressed as a voltage ratio (not in decibels). However, to completely characterise the reflection coefficient, the phase of ρ must also be found. This is done on a slotted line by measuring the distance of the first minimum from the DUT. Moving the probe right up to the DUT is not practicable so a different approach is usually adopted. The position of the first minimum when the reference short is in place is noted. The distance back along the line from this reference point to the next minimum when the DUT is in place will be the same as the distance from the DUT to the first minimum. This is so because the reference short guarantees a minimum at the DUT position.[13]
The phase part of ρ is given by,
where λ is the wavelength and x is the distance to the first minimum as described earlier. The magnitude and phase representation of ρ can, if required, be expressed as real and imaginary parts instead by the usual manipulation of complex numbers.[14]
Impedance
The impedance, Z, of the DUT can be calculated from the reflection coefficient by,
where Z0 is the characteristic impedance of the line. An alternative method is to plot the VSWR and distance to the node (in wavelengths) on a Smith chart. These quantities are directly measured by the slotted line. From this plot the DUT impedance (normalised to Z0) can be read directly off the Smith chart.[15]
Accuracy considerations
Good slotted lines are precision made instruments. They need to be because mechanical defects can affect accuracy. Some of the mechanical issues that are relevant to this include backlash of the vernier, concentricity of the inner and outer conductor, circularity of the outer conductor, centrality and straightness of the inner conductor, variations in cross-section, and the ability of the carriage to maintain a constant probe depth. Issues with probe tuning and disturbances to the field have already been discussed, but the insulated spacers holding the centre conductor in place can also disturb the field. Consequently, these are made as discrete as is compatible with mechanical strength. However, the greatest source of inaccuracy is usually not the slotted line itself, but the characteristics of the detector diode.[16]
The detected voltage signal output of the Schottky barrier diodes typically used in microwave detectors have a square law relationship to the power being measured and meters are calibrated accordingly. However, as the power increases, the diode deviates significantly from a square law and remains accurate up to an output voltage of only around 5-10 mV. This can be improved a little by adding a load resistor to the detector output, but this also has the undesirable effect of decreasing sensitivity. Another technique is to reduce the range of power being measured (so that it is brought within the square law range of the detector) by measuring at a point other than a maximum. The maximum is then calculated from the known mathematical shape of the standing wave pattern. This has the objection that it adds significantly to the labour required to make the measurements, as does the technique of precisely calibrating the detector and adjusting the readings on the meter according to a calibration chart.[17]
It is possible to completely eliminate errors in the detector and meter if a precision variable attenuator is used in the test setup. In this technique a minimum is first found and the attenuator adjusted so that the meter is indicating precisely some convenient mark. A maximum is then found and the attenuation increased until the meter is indicating the same mark. The amount the attenuation had to be increased is the VSWR of the standing wave. Accuracy here depends on the accuracy of the attenuator and not at all on the detector.[18]
Notes
- ^ Thomas H. Lee even describes a microstrip slotted line for use up to 5 GHz that he claims can be made for less than $10. He calls this a "40 dB cost reduction" over the price of a network analyser. That is, its cost is 10,000 times less than an analyser costing $100,000 (Lee, pages xv, 268-271).
- ^ λ, the customary symbol for wavelength. It is usually most convenient to give distances on transmission lines in terms of wavelengths of the transmitted wave, or sometimes, when the distance involved is small or not an exact multiple of a quarter wavelength, in radians where θ=2πλ radians.
- ^ square law, of a detector diode, the range over which the demodulated output voltage is proportional to the square of the carrier voltage on the line.
References
- ^ Multiple sources:
- Gupta, page 113
- Voltmer, pages 146–147
- ^ Multiple sources:
- Das & Das, page 496
- Lee, pages 246, 251, 268
- Voltmer, page 146
- ^ Multiple sources:
- Das & Das, pages 497–498
- Gupta, page 113
- ^ Voltmer, page 148
- ^ H. C. Torrey, C. A. Whitmer, Crystal Rectifiers, New York: McGraw-Hill, 1948
- ^ Das & Das, pages 496–498
- ^ Das & Das, pages 496–497
- ^ Multiple sources:
- Das & Das, page 496
- Voltmer, page 147
- ^ Gupta, pages 113–114
- ^ Voltmer, pages 147–148
- ^ Multiple sources:
- Das & Das, page 498
- Voltmer, page 148
- ^ Gupta, pages 112–113
- ^ Multiple sources:
- Gupta, pages 112–113
- Lee, pages 248–249
- ^ Multiple sources:
- Connor, pages 29–32
- Das & Das, page 498, 514-515
- Lee, pages 248–249
- ^ Multiple sources:
- Connor, pages 34–38
- Das & Das, pages 514–515
- Gupta, page 112, 114
- ^ Lee, pages 251–252
- ^ Lee, pages 252–254
- ^ Lee, page 253
Bibliography
- Connor, F. R., Wave Transmission, Edward Arnold Ltd., 1972 ISBN 0-7131-3278-7.
- Das, Annapurna; Das, Sisir K, Microwave Engineering, Tata McGraw-Hill Education, 2009 ISBN 0-07-066738-1.
- Gupta, K. C., Microwaves, New Age International, 1979 ISBN 0-85226-346-5.
- ISBN 0-521-83526-7.
- Voltmer, David Russell, Fundamentals Of Electromagnetics 2: Quasistatics and Waves, Morgan & Claypool, 2007 ISBN 1-59829-172-6.