Electromagnetic Fields and Waves: Notes, Solved Problems and Interactive Lab

Single-mode operation requires the frequency to lie above the cutoff of TE $_{10}$ and below the cutoff of the next mode,

f_{co, 10} < f < min (f_{co, 20}, f_{co, 01}), that is \frac{v}{2 a} < f < \frac{v}{a} when b \leq \frac{a}{2} . (7.3.43)

Commercial guides come in a standard series (Table 7.3.1). The WR number is the width $a$ in hundredths of an inch: WR-90 has $a = 0.900 in = 22.86 mm$ . Each guide has a recommended band of roughly $1.25$ to $1.9 f_{co, 10}$ , far enough above cutoff for low loss and low dispersion and safely below the next mode, and the height is $b \approx a /2$ , which gives the widest single-mode band together with the largest $ab$ (power) and $b$ (low loss).

Table 7.3.1. Standard rectangular waveguides (air filling, cutoffs with $c = 3 \times 1 0^{8} m/s$ ).

guide	$a \times b$ [mm]	band [GHz]	$f_{co, 10}$ / $f_{co, 20}$ [GHz]
WR-340	$86.36 \times 43.18$	$2.20$ – $3.30$	$1.74$ / $3.47$
WR-284	$72.14 \times 34.04$	$2.60$ – $3.95$	$2.08$ / $4.16$
WR-187	$47.55 \times 22.15$	$3.95$ – $5.85$	$3.16$ / $6.31$
WR-137	$34.85 \times 15.80$	$5.85$ – $8.20$	$4.30$ / $8.61$
WR-90	$22.86 \times 10.16$	$8.20$ – $12.4$	$6.56$ / $13.12$
WR-62	$15.80 \times 7.90$	$12.4$ – $18.0$	$9.49$ / $18.99$
WR-42	$10.67 \times 4.32$	$18.0$ – $26.5$	$14.06$ / $28.12$

The standard guides on a logarithmic frequency axis. Grey: the single-mode range from f_{co,10} (tick) to f_{co,20}. Green: the recommended band. Each guide covers about a factor of 1.5 in frequency, and neighbouring guides overlap. — **Figure 7.3.10.** The standard guides on a logarithmic frequency axis. Grey: the single-mode range from $f_{co, 10}$ (tick) to $f_{co, 20}$ . Green: the recommended band. Each guide covers about a factor of $1.5$ in frequency, and neighbouring guides overlap.

Quick check

Which standard guide would you choose for a $10 GHz$ link, and why not the next larger one?

WR-90: $10 GHz$ lies in its band, at $1.52 f_{co, 10}$ . WR-137 ( $f_{co, 20} = 8.61 GHz$ ) would carry TE $_{20}$ too at $10 GHz$ , and possibly TE $_{01}$ ( $9.49 GHz$ ): it is no longer single-mode.

7.3.7 Standard WR guides and the single-mode band