With an unknown load connected to a slotted air line, s = 2 is recorded by a standing wave indicator, and minima are found at 11 cm, 19 cm,... , on the scale. When the load is replaced by a short circuit, the minima are at 16 cm, 24 cm,... .If Zo = 50 Ω, calculate λ, f, and ZL.

Question

With an unknown load connected to a slotted air line, [latex]s = 2[/latex] is recorded by a standing wave indicator, and minima are found at [latex]11 cm, 19 cm,...[/latex], on the scale. When the load is replaced by a short circuit, the minima are at [latex]16 cm, 24 cm, ...[/latex]. If [latex]Z_{o}=50\Omega [/latex], calculate [latex]\lambda, f[/latex], and [latex]Z_{L}[/latex].

Accepted Answer

Consider the standing wave patterns as in Figure 11.23(a). From this, we observe that

[latex]\frac{\lambda}{2}=19-11=8 cm[/latex] or [latex]\lambda =16cm[/latex]

[latex]f=\frac{u}{\lambda}=\frac{3 imes 10^{8}}{16 imes 10^{-2}}=1.875GHz[/latex]

Electrically speaking, the load can be located at [latex]16 cm[/latex] or [latex]24 cm[/latex]. If we assume that the load is at [latex]24 cm[/latex], the load is at a distance [latex]\ell[/latex] from [latex]V_{min}[/latex], where

[latex]\ell=24-19=5cm=\frac{5}{16}\lambda=0.3125\lambda[/latex]

This corresponds to an angular movement of

[latex]0.3125 imes720^{\circ}=225^{\circ}[/latex]

on the [latex]s=2[/latex] circle.

By starting at the location of [latex]V_{min}[/latex] and moving 225° toward the load (counterclockwise), we reach the location of [latex]z_{L}[/latex] as illustrated in Figure 11.23(b). Thus

[latex]z_{L}=1.4+j0.75[/latex]

and

[latex]Z_{L}=Z_{o}z_{L}=50(1.4+j0.75)=70+j37.5\Omega[/latex]

Question 11.6: With an unknown load connected to a slotted air line, s = 2 ...

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