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Find the necessary condition for oscillations to occur and frequency of oscillations of colpitts oscillator. Also explain its working.
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• ColPiH is a high frequency tank ckt oscillator.

• It works on a principle of Barkhauson's criteria.

• In the given CKT Tx Q, along with Resi $R_1$, $R_2$, $R_c$ works as CE Ampli and provides phase - shift of 180˚

• Thus overall phase - shift around the loop is 360˚ or 0˚ which means ckt satisfies the barkhaunson's criteria and provides sinusoidal oscillation at the o/p

• The necessary condition for ckt to oscillate is that sum of all reluctance must be zero.

$Xc_1$ + $Xc_2$ + XL = 0

$\frac{-j}{wc_1}$ - $\frac{j}{wc_2}$ + jwl = 0

wl = $\frac{1}{w}$ $(\frac{1}{c_1}$ + $\frac{1}{c_2})$

Let $\frac{1}{c_1}$ + $\frac{1}{c_2}$ + $\frac{1}{ceq}$

$\therefore$ wl = $\frac{1}{wceq}$

$w^2$ = $\frac{1}{Lcwq}$

w = $\frac{1}{$\sqrt Lceq}$Moreover as per barkhaunson criteria | Av | ≥$\frac{Xc_1}{Xc_2}\therefore$|Av| ≥$\frac{c_2}{c_1}$![enter image description here][1] ![enter image description here][2] - In case of class A P.A we use restrictive load. - By using proper biasing ckt the transistor is operation at the center of load ? the active region. - Thus under no signal condition the TX is ON and when we apply the signal then TX conducts both for positive and negative half cycle ? conduction angle$\theta$= 0 to 360˚ - The efficiency of class A P.A is given as$\eta$=$\frac{poCAwemt}{picow}$pocawrms =$\frac{vo(p)}{\sqrt2}$=$\frac{I(p)}{\sqrt2}$Vo(p) = VCIQ =$\frac{Vcc}{2}$IO(p) = ICQ$\therefore$Po(AC)cms =$\frac{vcc.Icc}{4}$Pi(DC) = Vce. Icq$\therefore\eta$=$\frac{Vcc.ICQ/4}{Vcc.Icq}\eta$=$\frac{1}{4}$= 0.25$\therefore\eta\$ = 25%