Microwave waveguide and transmission line system
4.2 COMPONENTS
4.2.2 Waveguides
Waveguides are used for maximum power capacity and minimum losses. For each frequency band, there is a common size of waveguide that is the smallest reasonable size for the bandwidth involved. Oversized waveguides are used to reduce losses. The power carrying capacity of normal waveguides can be increased by filling them with desiccated compressed air and, if necessary, cooling them with water. Dry air under pressure (sometimes as low as 10 mbar) avoids condensation and corrosion that leads to additional losses. Often, even when air under pressure is not necessary, waveguides are filled with desiccated air to reduce corrosion and thus losses.
Waveguide losses are specified by the manufacturer per foot or per meter for the waveguide. To this must be added the flange losses. Runs with low loss use long waveguide sections to reduce the number of flanges and their losses.
Waveguides must be firmly attached to the supporting structure to avoid vibration, which would have a negative effect on the stability of the radar.
8cut-off ' 2 a fcut&off ' c
2 a
" ' B 2 F
,0 µ0
1 a3/2
2 f fc
&1/2
% a
b f fc
3/2
f fc
2
&1
Np/m
' B
2 F ,0 µ0
1 a3/2
2 f fc
&1/2
% a
b f fc
3/2
f fc
2
&1
20log10(e) dB/m
(4.3)
(4.4) Commonly decibels are used as a unit of loss. Decibels being logarithmic units, the total loss is the sum of the decibel values. A typical waveguide run for an air surveillance radar was shown in Figure 4.3 and connects the following:
• Transmitter output waveguide flange or connector.
This is the interface point where the transmitter power, pulse width, and spectrum are measured and have been found to be within tolerance.
• Antenna waveguide flange or connector.
This is the point where the antenna gain has been measured on the antenna measurement range. All components up to this point must be accounted for.
• Receiver input waveguide flange or connector.
This is the point where the receiver noise figure or temperature has been tested and accepted in the factory.
Individual manufacturers publish the characteristics of the components they make. The waveguides that connect them may be treated generically in terms of loss and power handling. Power handling is divided into peak power, which is limited by voltage breakdown, and average power, which is limited by cooling.
Normally, one waveguide size is used to connect the components. Waveguides carry radio frequency energy above their cut-off frequency. The cut-off wavelength for the TE10 mode is twice the broad dimension:
where a is the major dimension;
c is the velocity of light.
The useful frequency band is approximately 1.25 × fcut-off to 2 × fcut-off. For the standard S-band WR284 waveguide, the figures are as follows:
• Type WR284 waveguide;
• Inner dimension, a = 2.84 inches = 7.2135 cm;
• Cut-off wavelength = 14.4272 cm giving a cut-off frequency of 2 079.406 MHz;
• Frequency range is approximately from 2 600 MHz to 4 160 MHz.
The losses in an air-filled waveguide are caused mainly by the skin effect resistance of the internal walls. This is, theoretically, after [4, p. 65, Eq. 2-192]
where f is the working frequency, Hz;
f is the cutoff frequency, Hz;c
a and b are the major and minor waveguide dimensions, m;
F is the conductivity of the inner walls S/m;
,0 is the permittivity of free space;
µ is the permeability of free space.0
The theoretical losses are calculated in Figure 4.7 for WR284 (WG10) waveguide and two larger sizes (WR340 or WG9A) and WR439 (or WG8) for comparison. These are valid when the inner walls are very smooth.
0.005 0.01 0.015 0.02 0.025 0.03
2 3 4 5 6 7 8 9 10
Frequency, GHz Attenuation,
dB/m
Brass
Aluminium
Gold
Silver Recommended
frequency range WR284 or WG10
2.6 to 3.95 GHz
WR340, WG9A copper (2.2 to 3.3 GHz)
WR430, WG8 copper (1.7 to 2.6 GHz)
WR284 WG10
Copper
Maximum power ' Emax2 120B
8 8g
ab
4 W
Peak maximum power ' Peak power with perfect match (Voltage standing wave ratio)2
Figure 4.7 Waveguide attenuation in dB/m for WR284 waveguides with inner walls made of brass, aluminium, gold, copper, and silver and for copper WR340 and 430 waveguides.
(4.5)
(4.6) The waveguide tables [6] give two sizes of waveguide for most frequencies. In order to save size and weight, the smaller size is normally used, which gives greater attenuation; see Figure 4.7. For long lengths of waveguide it is often an advantage to choose a size where the working frequency is on the minimum point on the attention curve. These larger waveguides must be connected to the normal waveguides using long funnel-shaped transition waveguides.
The peak power in the waveguide is limited by the voltage breakdown between the broad sides. The normal breakdown voltage at sea level is approximately 30 kV/cm. The peak power in a waveguide in TE01 mode is with perfect matching [3, p. 179, Eq. 6.36]:
where Emax is the maximum electric field between the broad faces of the waveguide, V/m;
8 is the working wavelength, m;
8g is the guide wavelength, m;
a and b are the major and minor internal dimensions of the waveguide, m.
If this voltage is limited to 15 kV/cm (a safety factor of two), then the peak power in WR284 waveguide is defined in Figure 4.8.
Mismatch in the waveguide increases the peak voltage in the waveguide by the voltage standing wave ratio (VSWR).
The peak power able to be carried in the waveguide must be divided by this voltage ratio squared:
0 0.5 1.0 1.5 2.0 2.5
Peak power MW
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4
Frequency GHz Peak power at sea level 1013.25 HPa (mb), 25°C
Peak power at ca. 30 000 feet 300 HPa (mb), -40°C
Figure 4.8 Maximum peak power in WR284 waveguide at sea level and at 30 000 feet.
Normally, waveguides are filled with desiccated air at slightly above atmospheric pressure. The peak power carried by the waveguide may be increased if the pressure is increased. At a conservative estimate [7], the breakdown voltage is proportional to pressure and inversely proportional to the absolute temperature with respect to 30 KV/cm at 1 013.25 HPa (mb) and 25°C. This change is shown in Figure 4.8. A limit on the amount of air pressure that a waveguide can withstand is given by the manufacturer. For a time, high dielectric strength gases, such as sulfur hexafluoride (SF ), were6 used, but most produce toxic by-products after arcing and gas leaks in the waveguides caused problems. The maximum mean power is limited by the temperature rise and must be found from the manufacturer’s literature.
Commonly standard rectangular waveguides are used in the lowest mode. Feeds for circularly polarized waves ( see Section 5.6) must use waveguides that are symmetrical on both axes, namely, square or circular waveguides. Circular waveguides are also used as the central member of a rotating joint.