Contemplate the next illustration in Determine 1 of what we will see is an oscillator, particularly, a Colpitts oscillator.
Determine 1 The Colpitts oscillator the place the passive parts are organized on the right-hand facet for simpler viewing.
There’s an R-L-C community of passive parts and an energetic achieve block. For functions of this mannequin, the enter impedance of the achieve block is excessive sufficient for its loading impact to be ignored, the output impedance of the achieve block is zero and the worth of its achieve, A, is nominally unity or maybe rather less than unity. The resistance R1 fashions the output impedance {that a} real-world achieve block would possibly current.
To research this circuit, we take the passive parts, redraw them as on the appropriate and start utilizing node evaluation (Determine 2). The time period G1 = 1 / R1 and the time period S = j / (2*π*F).
Determine 2 Node evaluation used for circuit offered on the right-hand facet of Determine 1.
Having gotten the connection between Eo and E1 to the exclusion of E2, we do a number of algebraic steps to get that relationship right into a helpful type as proven in Determine 3.
Determine 3 An algebraic rearrangement the place the switch perform is introduced right into a extra helpful type.
Observe that the denominator of this final equation is cubic. It’s a third order polynomial as a result of there are three unbiased reactive components within the circuit, L1, C1 and C2.
Please additionally notice that the order of the polynomial MUST match the variety of unbiased reactive components within the circuit. If we had provide you with 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 4.
Determine 4 A plot of E1/Eo versus frequency from algebraic evaluation in Determine 3.
The switch perform of the passive R-L-C community has a pronounced peak at a frequency of 1.59 MHz. After we run a SPICE simulation of that switch perform, we discover the identical consequence (Determine 5).
Determine 5 A SPICE evaluation of the passive R-L-C community exhibiting E1/Eo versus frequency with an outlined peak of virtually 40 dB at 1.59 MHz.
After we let our achieve block be a voltage follower, a JFET supply follower as proven in Determine 6, we see oscillation at very practically the frequency of that switch perform peak.
Determine 6 Colpitts oscillator constructed from passive community proven in Determine 5 by introducing a JFET supply follower, that displays the frequency of the switch perform peak.
John Dunn is an electronics marketing consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York College (MSEE).
Associated Content material
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- JFETs supply LC oscillators with few parts
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