Having already examined the Colpitts oscillator, we now take a look at its first cousin, the Clapp oscillator.
Please take into account the next illustration in Determine 1.
Determine 1 A Clapp oscillator the place the passive elements are organized on the right-hand aspect for simpler viewing. Supply: John Dunn
There may be an R-L-C community of passive elements and an energetic acquire block. This circuit differs from the Colpitts by now utilizing a 3rd capacitor (C3) in sequence with the inductance (L1) and by now needing a DC path: R2, to floor for the acquire block. The output impedance of the acquire block is zero and the worth of its acquire (A) is nominally unity or maybe rather less than unity. The resistance R1 fashions the output impedance {that a} real-world acquire block may current.
To investigate this circuit, we take the passive elements, redraw them as on the proper in Determine 1 and the place G1 = 1 / R1, G2 = 1 / R2, and the time period S = j / ( 2*π*F), we use node evaluation to derive the switch perform E1 / Eo.
The evaluation for the Clapp circuit is reasonably extra concerned than it was for the Colpitts circuit so for the sake of readability, I’ve omitted it right here. Nevertheless, my handwritten notes of that evaluation may be seen on the finish of this essay. Strive to not pressure your eyes.
The top result’s an expression of the switch perform in a helpful kind as follows in Determine 2.
Determine 2 Algebraic expression of switch perform for the Clapp oscillator proven in Determine 1. Supply: John Dunn
Be aware that the denominator of this equation is fourth order. It’s a fourth order polynomial as a result of there are 4 unbiased reactive components within the circuit, L1, C1, C2 and C3.
Please additionally notice that the order of the polynomial MUST match the variety of unbiased reactive components within the circuit. If we had give you an algebraic expression of another order, we’d know we’d made a mistake someplace.
Graphing the ratio of E1/Eo versus frequency, we see the next in Determine 3.
Determine 3 E1/Eo versus frequency from algebraic evaluation. Supply: John Dunn
The switch perform of the passive R-L-C community has a pronounced peak at a frequency of 1.62 MHz and a null at a barely decrease frequency. Once we run a spice simulation of that switch perform, we discover very almost the identical end result (Determine 4). I blame the variations on software program numerical accuracy points.
Determine 4 E1/Eo versus frequency from SPICE Evaluation. Supply: John Dunn
Once we let our acquire block be a voltage follower—a JFET supply follower within the following instance—we see oscillation on the frequency of that switch perform peak as proven in Determine 5.
Determine 5 Clapp Oscillator simulation after letting our acquire block be a voltage follower. Supply: John Dunn
The algebraic derivation of the Clapp oscillator switch perform is proven in handwriting in Determine 6.
Please forgive the handwriting. I simply didn’t have the endurance to show this right into a printout.
Determine 6 John Dunn’s switch perform derivation. Supply: John Dunn
John Dunn is an electronics advisor, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York College (MSEE).
Associated Content material
- The Colpitts oscillator
- Emitter followers as Colpitts oscillators
- Simulation hassle: Bode plotting an oscillator
- Oscillator has voltage-controlled responsibility cycle
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