Introduction:

A phase-shifting circuit is often employed to correct an undesirable phase shift already present in a circuit or to produce special desired effects. An RC circuit is suitable for this purpose because its capacitor causes the circuit current to lead the applied voltage. Two commonly used RC circuits are (RL circuits or any reactive circuits could also serve the same purpose.) In the circuit current I leads the applied voltage by some phase angle where depending on the values of R and C. If then the total impedance is and the phase shift is given by

circuit Diagram:

Working:Intuitively, the phase shifter uses a first-order low-pass filter to create a phase shift and negative feedback to compensate for non-unity gain. The result is an all-pass filter that has input-to-output quadrature (i.e., quarter-wavelength, or 90◦, phase shift) at ω =

1/(RC) (i.e., f = 1/(2πRC)).

1. Node A forms a low-pass filter (LPF) with transfer function1

HLPF(s) = 1

sRC+1 and so VA(s) = Vin(s)HLPF(s).

2. Because the op. amp. (OA) has negative feedback, VB(s) _ VA(s) (i.e., node B matches node A ).So the current into node B is

3. The current into node A does not go into the OA, and so it goes across the feedback resistor and sets up the output. The output at node C must then be

So the transfer function of the system is H(s) , (1 − sRC)/(1 + sRC). For any ω,

|H(jω)| = 1 and ∠H(jω) = arctan(−ωRC) − arctan(ωRC) = −2 arctan(ωRC),

which is double the LPF phase shift ∠HLPF(jω) = −arctan(ωRC). Note that

0 if ω = 0 (i.e., open capacitor — follower with no shift at DC),

∠H(jω) = −π /2 = −90◦ if ω = 1 /RC (i.e., quadrature — 90◦ shift at LPF corner),

−π = −180◦ as ω → ∞ (i.e., short capacitor — inverting amplifier at AC).

This circuit is an all-pass filter; it provides frequency-dependent phase shift with unity gain.

Components : 1. 5.1k ohms resistor (2)

2. potentiometer 2k ohms

3. operational amplifier 741

4. capacitor 47nF

5. Function Generator

6. Oscilloscope

Resistors are used in constructing negative feedback with operational amplifier the purpose is to

maintain the stable output which is equal to output. In addition to it Function Generator to give

power to phase shifter and oscilloscope to observe and analyze the output of phase shifter

LTSpice simulation:

Circuit Diagram in LTSpice

Results:

For R=0 ohm

For R=500 ohms

For R=1000 ohms

For R=5000 ohms

For R=10000 ohms

Conclusion:This circuit is used in RF and microwave Phase Shifters have many applications in various

equipments such as phase discriminators, beam forming networks, power dividers, linearization

of power amplifiers, and phase array antennas. If the position of R1 and C1 are reversed, the

phase then varies reversely.

project Topic:

Phase-Shifter

submitted by:

Numan Abdullah

DDP-SP14-BEE-025

Submited to:

Sir Masood Ahmed

Department of Electrical Engineering