Free Hartley & Colpitts LC Oscillator Calculator
Calculate resonant frequency, tank impedance, feedback ratio, and minimum sustaining voltage gain (Av) for Colpitts and Hartley LC oscillators.
📻 Oscillator Circuit Configuration
Equivalent Tank Capacitance: 180.3 pF
• Resonant Tank Impedance (R_p): 12.3 kΩ (R_p = Q • ωL).
• Recommended Starting Gain: ≥ 13.6 V/V (22.7 dB) (3× Barkhausen minimum for reliable start-up).
Design Tip: In Colpitts oscillators, choosing $C_2$ between 3× and 5× greater than $C_1$ ensures adequate loop gain while presenting high impedance to the collector, minimizing tank harmonic distortion.
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Barkhausen Stability Criteria for LC Oscillators
For a feedback amplifier to sustain sinusoidal oscillation at a specific frequency $f_0$, it must satisfy Barkhausen's two criteria:
- Loop Gain Magnitude: The open-loop gain product must be unity: $|A_v cdot eta| ge 1$.
- Loop Phase Shift: Total closed-loop phase shift around the feedback loop must be exactly $0^circ$ or $360^circ$. For an inverting amplifier ($180^circ$), the LC feedback network must provide the remaining $180^circ$ phase shift.
Colpitts vs. Hartley Governing Formulas
Colpitts Frequency: f_0 = 1 / (2π √(L × C_eq))
Colpitts Feedback: β = C_1 / C_2 &implies; A_v(min) = C_2 / C_1
Hartley Eq L: L_eq = L_1 + L_2 + 2M
Hartley Frequency: f_0 = 1 / (2π √(L_eq × C))
Hartley Feedback: β = (L_1 + M) / (L_2 + M) &implies; A_v(min) = (L_2 + M) / (L_1 + M)
Why Colpitts Is Favored at High Radio Frequencies
At VHF and UHF frequencies, the internal parasitic capacitances of active devices (BJT $C_{be}$ and $C_{ce}$, or MOSFET $C_{gs}$ and $C_{ds}$) swamp high-impedance nodes. In a Colpitts oscillator, these stray capacitances sit directly in parallel with external capacitors $C_1$ and $C_2$, meaning they can simply be subtracted from the physical component values without causing parasitic oscillations or unpredictable detuning.
Frequently Asked Questions
What happens if the amplifier gain Av is much higher than the minimum requirement?
If Av >> Av(min), the circuit starts oscillating aggressively, but the excessive loop gain quickly drives the transistor into deep saturation and cutoff clipping. This produces severe odd-harmonic distortion (sine wave clipping into a trapezoid). For clean sinusoidal output, designers often use an automatic gain control (AGC) loop or JFET limiter.
How does mutual inductance M affect a Hartley oscillator?
When L1 and L2 are wound as a single continuous tapped coil on a shared toroid or ferrite rod, mutual coupling M is significant. For series-aiding turns, the total inductance increases to Leq = L1 + L2 + 2M, pulling the resonant frequency lower than uncoupled discrete inductors.
Why does my oscillator fail to start in bench testing?
The most common causes are: (1) active device transconductance gm is too low to overcome tank parallel loss resistance Rp; (2) inductor Q is lower than estimated; or (3) load impedance connected to the tank is pulling down the loaded Q.