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UPPCL JE EC 25 March 2021 Official Paper (Shift 2)

Option 4 : \(\dfrac{ \phi+\pi \mp cos^{-1} |K| }{\pi}. \dfrac{\lambda}{4}\)

**Explanation:**

**1. **Stub tuning is an impedance matching technique when an open-circuited or short-circuited transmission line is connected to the main transmission line.

**2**. Stub matches are widely used to match any complex load to a transmission line.

**3.** In a transmission line, to match the complex load to the transmission line stub matching is used.

There are two types of stub matching:

- Short circuit stub
- Open circuit stub

These stubs can be connected to the transmission line either in series or parallel with a fixed distance from the load.

- Generally short-circuit stubs are more preferred compared to the open circuit stub, because open-circuit stubs may radiate as their ends are open.
- Characteristic’s impedance of stub and line should be the same.

Where, Z0 = characteristics impedance of transmission line (Ω)

d = distance of stub from load end (m)

L = length of the stub (m)

Identify a position on the line from the load where Z = Z_{o} ± jx then x value is 'd' position of the stub.

\(d=\frac{\lambda}{4\pi}tan^{-1}\sqrt {\frac{Z_L}{Z_o}}\)

The point of location of a short-circuited stub on the line is also given by:

\(d=\dfrac{ \phi+\pi \mp cos^{-1} |K| }{\pi}. \dfrac{\lambda}{4}\)

\(Where \ K=\frac{Z_L-Z_o}{Z_L+Z_o}\)

Hence **option (4)** is the correct answer.