Find the necessary condition for oscillations to occur and frequency of oscillations of colpitts oscillator. Also explain its working.
1 Answer
  • 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%

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