Transmission Lines Measurements: High Frequencies

TRANSMISSION LINES MEASUREMENTS: HIGH FREQUENCIES LECTURE 7

■ Microwaves are a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter; with frequencies between 300 MHz (1 m) and 300 GHz (1 mm). ■ microwaves include the entire SHF band (3 to 30 GHz, or 10 to 1 cm) at minimum. 2

■ Microwaves travel by line-of-sight; unlike lower frequency radio waves they do not diffract around hills, follow the earth's surface as ground waves, or reflect from the ionosphere, so terrestrial microwave communication links are limited by the visual horizon to about 40 miles (64 km).

■ At limiting practical communication distances to around a kilometer.

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■ Microwaves are widely used in modern technology, for example in ■ ■ ■ ■ ■ ■ ■ ■ ■ ■

point-to-point communication links, wireless networks, microwave radio relay networks, radar, satellite and spacecraft communication, medical diathermy and cancer treatment, remote sensing, radio astronomy, collision avoidance systems, garage door openers, and for cooking food in microwave ovens. 4

Name

Wavelength

Frequency (Hz)

Gamma ray X-ray

< 0.02 nm 0.01 nm – 10 nm

> 15 EHz 30 EHz – 30 PHz

Ultraviolet

10 nm – 400 nm

30 PHz – 750 THz

Visible light

390 nm – 750 nm

770 THz – 400 THz

Infrared

750 nm – 1 mm

400 THz – 300 GHz

Microwave

1 mm – 1 m

300 GHz – 300 MHz

Radio

1 mm – 100 km

300 GHz – 3 kHz

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• At microwave frequencies, the transmission lines which are used to carry lower frequency radio waves to and from antennas, such as coaxial cable and parallel wire lines, have excessive power losses, so when low attenuation is required microwaves are carried by metal pipes called waveguides. • Due to the high cost and maintenance requirements of waveguide runs, in many microwave antennas the output stage of the transmitter or the RF front end of the receiver is located at the antenna. 6

■ Transmission lines and waveguides are used to transmit electric energy and signals from one point to another, specifically from a source to a load. ■ Any media that can support a electromagnetic wave has a characteristic impedance associated with it. ■ Although characteristic impedance units are in Ohms, it is not a "real" impedance you can measure using direct current equipment such as a DC Ohmmeter.

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Transmission Lines ■ The propagation constant for the uniform plane wave

• Characteristic impedance Zo

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■ Example

■ A lossless transmission line is 80 cm long and operates at a frequency of 600 MHz. The line parameters are L=0.25 µH/m and C = 100 pF/m. Find the characteristic impedance, the phase constant, the velocity on the line, and the input impedance for ZL = 100 Ω Since the line is lossless, both R and G are zero. The characteristic impedance

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Reflection Coefficient ■ The propagation of electromagnetic energy can generally be regarded as wave propagation. ■ A particularly simple type of wave is one which travels along a straight line, following a uniform path or waveguide. ■ The wave has sinusoidal time variation at a single frequency and may suffer attenuation due to dissipation but is not reflected unless it encounters some discontinuity in, or termination of, the path or waveguide.

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■ The reflection of a wave traveling in one direction may in general produce a scattering, such that waves in different modes are set up in different directions. ■ However, for our purposes, only the wave coming back along the same path in the same mode is regarded as the reflected wave, the others being regarded as scattered wave components.

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■ If the incident and reflected wave amplitudes are denoted by a and b, respectively, the reflection coefficient is the ratio of b to a. Reflection coefficient = reflected incident ■ Since the wave amplitudes are usually written in complex form to include phase information regarding the sinusoidal time variation, the reflection coefficient, Γ as defined above is, in general, complex. 13

WAVE REFLECTION AT DISCONTINUITIES ■ The concept of a reflected wave originates from the necessity to satisfy all voltage and current boundary conditions at the ends of transmission lines and at locations at which two dissimilar lines are connected to each other.

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■ The consequences of reflected waves is that some of the power that was intended to be transmitted to a load, for example, reflects and propagates back to the source. ■ The basic reflection problem is illustrated in Figure.

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■ In it, a transmission line of characteristic impedance Z0 is terminated by a load having complex impedance, ZL = RL + j XL. ■ For convenience, we assign coordinates such that the load is at location z = 0. ■ Therefore, the line occupies the region z < 0. ■ A voltage wave is presumed to be incident on the load, and is expressed in phasor form for all z: Where, β is the phase constant, and α is the attenuation constant 16

VOLTAGE STANDING WAVE RATIO ■ Knowing the reflection coefficient, we may find the standingwave ratio.

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■ One of the important basic measuring instruments used at ultra-high frequencies is the slotted line.

■ With it, the standing-wave pattern of the electric field in coaxial transmission line of known characteristic impedance can be accurately determined. ■ In many instances, characteristics of transmission line performance are amenable to measurement.

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■ Included in these are measurements of unknown load impedances, or input impedances of lines that are terminated by known or unknown load impedances. ■ Such techniques rely on the ability to measure voltage amplitudes that occur as functions of position within a line, usually designed for this purpose. ■ A typical apparatus consists of a slotted line, which is a lossless coaxial transmission line having a longitudinal gap in the outer conductor along its entire length. 20

■ The line is positioned between the sinusoidal voltage source and the impedance that is to be measured. ■ Through the gap in the slotted line, a voltage probe may be inserted to measure the voltage amplitude between the inner and outer conductors. ■ As the probe is moved along the length of the line, the maximum and minimum voltage amplitudes are noted, and their ratio, known as the voltage standing wave ratio, or VSWR, is determined. 21

■ From the knowledge of the standing-wave pattern several characteristics of the circuit connected to the load end of the slotted line can be obtained. ■ For instance, the degree of mismatch between the load and the transmission line can be calculated from the ratio of the amplitude of the maximum of the wave to the amplitude of the minimum of the wave. ■ This is called the voltage standing-wave ratio, VSWR.

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■ The load impedance can be calculated from the standing wave ratio and the position of a minimum point on the line with respect to the load. ■ The wavelength of the exciting wave can be measured by obtaining the distance between minima, preferably with a lossless load to obtain the great resolution, as successive minima or maxima are spaced by half wavelengths.

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■ Let us assume that we have made experimental measurements on a 50 slotted line that show there is a voltage standing wave ratio of 2.5. ■ This has been determined by moving a sliding carriage back and forth along the line to determine maximum and minimum voltage readings.

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■ A scale provided on the track along which the carriage moves indicates that a minimum occurs at a scale reading of 47.0 cm, as shown in Figure.

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■ The location of the minimum is usually specified instead of the maximum because it can be determined more accurately than that of the maximum; think of the sharper minima on a rectified sine wave. ■ For example, if the frequency of operation is 400 MHz, so the wavelength is 75 cm.

■ In order to pinpoint the location of the load, we remove it and replace it with a short circuit; the position of the minimum is then determined as 26.0 cm. 26

■ We know that the short circuit must be located an integral number of half wavelengths from the minimum; let us arbitrarily locate it one half-wavelength away at 26.0 − 37.5 = −11.5 cm on the scale. ■ Since the short circuit has replaced the load, the load is also located at −11.5 cm.

■ Our data thus show that the minimum is 47.0 − (−11.5) = 58.5 cm from the load, or subtracting one-half wavelength, a minimum is 21.0 cm from the load. 27

■ The voltage maximum is thus 21.0−(37.5/2) = 2.25 cm from the load, or 2.25/75 = 0.030 wavelength from the load.

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