Comments on Results of analysis of Hartley oscillator dont make sense
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Results of analysis of Hartley oscillator dont make sense
I want to find the conditions of oscillation of the following Hartley oscillator.I have attached a load (ZL) to my Hartley oscillator
I have written KCL for nodes A,B:
For node A:
$$\frac{V_{A}}{sL_{1}} + \frac{V_{A}}{Z_{L}}+\frac{V_{A}}{R_{C}}-sC_{1}(V_{A}-V_{B})+g_{m}V_{x} = 0 \rightarrow V_{A}(Z_{L}R_{C}+sL_{1}R_{C}+sL_{1}Z_{L})-sC_{1}sL_{1}R_{C}Z_{L}(V_{B}-V_{A})+g_{m}V_{B} = 0 \rightarrow (g_{m}-sL_{1}sC_{1}R_{C}Z_{L})V_{B} = (-sL_{1}sC_{1}R_{C}Z_{L}-R_{C}Z_{L}-sL_{1}R_{C}-sL_{1}Z_{L})V_{A}$$
But $$\frac{V_{o}}{V_{in}} = 1 \rightarrow $$
$$g_{m}-sL_{1}sC_{1}R_{C}Z_{L} = -sL_{1}sC_{1}R_{C}Z_{L}-R_{C}Z_{L}-sL_{1}R_{C}-sL_{1}Z_{L} \rightarrow g_{m} = -R_{C}Z_{L} , -sL_{1}R_{C} = sL_{1}Z_{L} $$
which doesnt make any sense.Where am I doing wrong in my analysis?
Post
This LC circuit depends on several criteria for stable linear oscillation;
- 180 deg phase shift ( with 3rd order LC network) plus 180 degree inversion to achieve the oscillation criteria of 0 or 360 deg at gain >=1 Thus each reactance affects fo.
- adequate bias current and impedance ratios with negative feedback ratios at DC and at fo.
- Only 1 capacitor is necessary
A variation was made by adding the L1,L2 ground resistance for a notch filter effect.
- keeping the resistance ratios of R2/R3=1.5 to 3 range that affects feedback attenuation and impedance range used to satisfy requirements.
- The feedback cap. and H bias were also replaced with one feedback resistor, R2
- By tuning hFE to lower values, one can improve R ratios for sufficient gain to oscillate with pull up/down for a symmetrical sine wave.
- Excess gain will clip the sine wave.
The sensitivity to each resistance part value in the simulation gives more insight than the math and leads to a stable result. In reality, hFE is nonlinear with current, but I did add a slider for constant hFE = 10 to 50.
The highlight of this answer is to show the results of resistance ratios and hFE can be significant.
This design is not intended to be ideal, and there are better designs that have much higher Q for square wave clocks or nonlinear feedback for sine amplitude unity-gain AGC-like control.
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