Colpitts Oscillator
The Colpitts oscillator is one of the most widely used RF oscillator circuits in radio engineering. Named after Edwin Colpitts, who patented it in 1918, it appears in VFOs, BFOs, local oscillators, signal generators and test equipment across the frequency range from a few hundred kilohertz up to several gigahertz. Its defining feature is a capacitive voltage divider that both selects the oscillation frequency and provides the feedback signal to sustain oscillation.
- The LC Tank Circuit — A Brief Recap
- The Colpitts Topology — Capacitive Voltage Divider
- The Frequency Formula
- Feedback Ratio and Component Selection
- Worked Examples at Ham Radio Frequencies
- Colpitts Frequency Calculator
- The Clapp Oscillator — A More Stable Variant
- Practical Design Notes for Amateur Radio
The LC Tank Circuit — A Brief Recap
An LC tank circuit consists of an inductor (L) and a capacitor (C) connected in parallel. At a specific frequency — the resonant frequency — the inductive reactance equals the capacitive reactance and they cancel each other out. At resonance the impedance of the parallel combination is very high, while just off resonance the impedance drops sharply.
Energy oscillates back and forth between the magnetic field of the inductor and the electric field of the capacitor. If no losses were present, this would continue forever — a perfect lossless tank. In reality, the inductor's wire resistance and other losses gradually damp the oscillation. An active device (a transistor or FET) connected to the tank can replenish the energy lost on each cycle, sustaining the oscillation indefinitely.
The resonant frequency of a simple LC tank is:
f = 1 / (2π × √(L × C))
Where: f = frequency in Hz, L = inductance in henries, C = capacitance in farads
The Colpitts Topology — Capacitive Voltage Divider
In a Colpitts oscillator, the single capacitor in the basic LC tank is replaced by two capacitors in series — typically called C1 and C2. The junction between C1 and C2 provides the feedback voltage. The inductor connects from the top of C1 to ground, and the transistor's collector (or drain, for a FET version) connects to the same top point. The emitter (or source) connects to the midpoint between C1 and C2, and the base (or gate) is connected to ground for AC through a bypass capacitor.
This arrangement is a capacitive voltage divider. The signal voltage across the entire tank (from the collector connection to ground) is divided down by the ratio C1/(C1+C2). The smaller portion appears at the emitter — which is the feedback point. This feedback is in the correct phase: the common-base (or common-gate) configuration used here does not invert the signal, so the feedback is positive without needing any additional phase inversion.
Think of it this way: the inductor and the series combination of C1 and C2 form the resonant tank. The feedback tap at the C1/C2 junction is like a voltage tap on a potential divider — it samples a fraction of the tank voltage and returns it to the transistor's emitter to keep the oscillation going.
Complete Colpitts oscillator schematic. The tank circuit consists of inductor L with capacitors C1 and C2 in series. The feedback signal is taken from the junction of C1 and C2 and returned to the transistor emitter. The output is taken from the collector through a coupling capacitor to a buffer amplifier.
View LargerThe Frequency Formula
Because C1 and C2 are in series across the inductor, the total capacitance seen by the inductor is their series combination. The series capacitance formula is:
Cseries = (C1 × C2) / (C1 + C2)
This is smaller than either individual capacitor — just as resistors in parallel give a lower resistance than either alone, capacitors in series give a smaller capacitance than either alone.
The oscillation frequency is then:
f = 1 / (2π × √(L × Cseries))
where Cseries = (C1 × C2) / (C1 + C2)
Combined: f = 1 / (2π × √(L × C1×C2/(C1+C2)))
The Colpitts tank circuit in detail. The effective capacitance in the resonant circuit is C1 and C2 in series. The feedback voltage at the C1/C2 junction is a fraction of the full tank voltage, determined by the capacitor ratio.
View LargerFeedback Ratio and Component Selection
The feedback fraction — the ratio of the feedback voltage to the full tank voltage — is determined by the capacitor values. For the standard Colpitts topology (emitter at the C1/C2 junction, collector at the top of the tank):
β = C2 / (C1 + C2)
Wait — why C2 and not C1? Because the feedback voltage appears across C1 (between the C1/C2 junction and the top of the tank where the collector connects). Voltage divider: VC1 / Vtank = XC1 / (XC1 + XC2) = C2 / (C1 + C2) (at resonance, reactances are inversely proportional to capacitance).
For reliable oscillation the amplifier gain (A) must exceed 1/β. If β is too small (large C1, tiny C2), more gain is needed. If β is too large, amplitude limiting becomes harsh. A feedback fraction of 0.1 to 0.3 (10% to 30%) works well in most LC Colpitts designs with transistor voltage gains of 20 to 100.
Practical component selection guidelines:
- Use C1 larger than C2 (ratio of 5:1 to 10:1 is typical) for moderate feedback
- The series combination Cseries sets the frequency alongside L
- Use a variable capacitor in series with (or as part of) L for tunable VFOs
- Use high-Q capacitors (silver-mica, NP0/C0G ceramic) in the tank for minimum frequency drift
- Keep the inductor Q high: use air-core or toroidal cores for HF, air-core solenoids for VHF
Worked Examples at Ham Radio Frequencies
Design a Colpitts VFO for the 40-meter amateur band centred near 7.1 MHz.
Choose components:
L = 1.0 μH (wound on T50-6 toroidal core)
C1 = 470 pF (feedback capacitor)
C2 = 100 pF (tank capacitor to ground)
Step 1 — Calculate Cseries:
Cseries = (C1 × C2) / (C1 + C2) = (470 × 10³ pF × 100 × 10³ pF) / (470 + 100) pF
Wait — these are both in pF, so:
Cseries = (470 × 100) / (470 + 100) = 47,000 / 570 = 82.46 pF = 82.46 × 10-12 F
Step 2 — Calculate frequency:
f = 1 / (2π × √(1.0 × 10-6 × 82.46 × 10-12))
= 1 / (2π × √(82.46 × 10-18))
= 1 / (2π × 9.081 × 10-9)
= 1 / (57.06 × 10-9)
= 17.53 × 106 Hz = 17.53 MHz
That's higher than 7 MHz. We need to adjust. For 7 MHz with L = 1 μH:
Cseries needed = 1 / (4π² × f² × L) = 1 / (4 × 9.87 × 49 × 1012 × 1 × 10-6)
= 1 / (1935 × 106) = 517 pF
Now choose C1 and C2 that give 517 pF series:
Try C1 = 2200 pF, C2 = 620 pF:
Cseries = (2200 × 620) / (2200 + 620) = 1,364,000 / 2820 = 483.7 pF — slightly low.
Try C1 = 1500 pF, C2 = 1000 pF:
Cseries = (1500 × 1000) / (1500 + 1000) = 1,500,000 / 2500 = 600 pF — too high.
Try C1 = 1800 pF, C2 = 680 pF:
Cseries = (1800 × 680) / (1800 + 680) = 1,224,000 / 2480 = 493.5 pF — close.
f = 1 / (2π × √(1 × 10-6 × 493.5 × 10-12)) = 1 / (2π × 2.221 × 10-8) = 7.17 MHz ✓
Feedback fraction: β = C2/(C1+C2) = 680/2480 = 0.274 (27%) — well within the practical range.
At VHF, component values are much smaller. Target 144.2 MHz with L = 50 nH.
Find required Cseries:
Cseries = 1 / (4π² × (144.2 × 106)² × 50 × 10-9)
= 1 / (4 × 9.87 × 20,793.64 × 1012 × 50 × 10-9)
= 1 / (4 × 9.87 × 1039.68 × 103)
= 1 / (41,044 × 103) = 24.36 pF
Choose C1 = 100 pF, C2 = 33 pF:
Cseries = (100 × 33) / (100 + 33) = 3300 / 133 = 24.81 pF
f = 1 / (2π × √(50 × 10-9 × 24.81 × 10-12)) = 142.9 MHz — very close to 144 MHz.
Reducing L slightly to 48 nH brings it exactly on frequency.
At VHF, even the lead inductance of component wires (a few nanohenries) is significant — components must be mounted with very short leads directly on a ground plane.
Colpitts Oscillator Frequency Calculator
Colpitts Oscillator Frequency Calculator
Enter the inductance and both capacitor values to calculate the oscillation frequency. The series combination of C1 and C2 forms the effective tank capacitance.
The Clapp Oscillator — A More Stable Variant
The Clapp oscillator (also called the Clapp-Gouriet oscillator) is a refinement of the Colpitts that improves frequency stability by reducing the influence of the transistor's internal capacitances on the oscillation frequency.
In the standard Colpitts, the transistor's collector-base and emitter-base junction capacitances are part of the tank circuit. These capacitances vary with temperature and with the instantaneous signal voltage, introducing frequency instability. The Clapp oscillator solves this by adding a third capacitor (C3) in series with the inductor. C3 is made much smaller than C1 and C2. Because the series combination of C1, C2, and C3 is dominated by the smallest value (C3), and C3 is a fixed, high-quality capacitor (not part of the transistor), the transistor's capacitances have much less effect on the total tank capacitance.
The Clapp frequency formula is the same as Colpitts, but with three capacitors in series:
Ctotal = 1 / (1/C1 + 1/C2 + 1/C3)
f = 1 / (2π × √(L × Ctotal))
In practice, when C3 << C1 and C3 << C2, the formula simplifies to approximately f = 1/(2π√(LC3)) — the frequency is dominated by L and C3 alone, making it highly stable. The Clapp oscillator is an excellent choice for a fixed-frequency or narrowly-tunable VFO where stability is the priority.
Practical Design Notes for Amateur Radio
Building a working Colpitts VFO for the amateur bands is within the reach of any beginner with access to basic components and a frequency counter. Here are the key principles:
Transistor selection: Any general-purpose NPN transistor with adequate gain-bandwidth product (fT) for the intended frequency works. At HF (below 30 MHz), 2N2222, 2N3904, or 2N4124 are all suitable. At VHF (144 MHz and above), use a transistor specified for RF use such as 2N5179, BFR90, or BFR96, which have fT values above 1 GHz.
Inductor Q: At HF, winding on a powdered-iron toroidal core (T50-6 or T68-6 for 10–50 MHz, T50-2 or T68-2 for 1–30 MHz) gives Q values of 100–300. At lower HF, air-wound coils on a polystyrene former also work well. The inductor is the single biggest contributor to tank Q and therefore frequency stability.
Capacitor quality: Use silver-mica or NP0/C0G ceramic capacitors for C1 and C2. These have excellent temperature stability (near-zero temperature coefficient) and low loss (high Q). Never use Y5V or Z5U ceramic capacitors in the tank — their capacitance can change 50% with temperature, making the oscillator drift severely.
Power supply: Regulate the transistor supply voltage to ±1% or better. Use a zener diode regulator or a three-terminal regulator (78L05 for 5 V, 78L08 for 8 V) dedicated to the oscillator stage. Supply voltage changes alter transistor capacitances and bias point, shifting frequency.
Buffer isolation: Never connect a load directly to the oscillator tank. Use an emitter follower or common-base buffer amplifier between the oscillator and the load. The buffer's high input impedance prevents the load from pulling the oscillator frequency.
⚖ Experiment: Build a 3.5 MHz Colpitts Oscillator
Build a simple Colpitts oscillator for the 80-meter amateur band (3.5 MHz) and measure its frequency with a frequency counter or amateur transceiver.
- 2N3904 NPN transistor
- Inductor: T50-2 toroidal core wound with 20 turns of #28 enamelled wire (approximately 2.5 μH)
- C1 = 2200 pF silver-mica capacitor
- C2 = 470 pF silver-mica capacitor
- Bias resistors: R1 = 47 kΩ, R2 = 10 kΩ
- Emitter resistor: Re = 470 Ω
- Decoupling capacitor: 0.1 μF ceramic (supply bypass)
- Coupling capacitor: 10 pF for output
- 9 V battery with regulator or 8 V supply
- Breadboard
- Frequency counter or a friend with an HF transceiver to identify the signal
- Wind the inductor: thread the core onto the wire and wind 20 turns through the hole. The wire should occupy about 3/4 of the toroid. Measure inductance if you have an LC meter; it should be approximately 2.5 μH.
- Wire the transistor in common-base configuration: base grounded through a 0.1 μF bypass cap, emitter at the C1/C2 junction, collector at the top of L.
- Connect R1 from +8V to the collector, R2 from +8V to the base, Re from emitter to ground.
- C1 from collector to the C1/C2 junction, C2 from the C1/C2 junction to ground. L from collector to ground.
- Connect a 10 pF coupling cap from the collector to your frequency counter or oscilloscope probe.
- Apply power. Measure the output frequency.
Expected frequency: Cseries = (2200 × 470)/(2200+470) = 387 pF. f = 1/(2π√(2.5×10⁻⁶ × 387×10⁻¹²)) = 1/(2π × 31.12×10⁻⁹) = 5.11 MHz. Adjust the winding to 28 turns (about 4.8 μH) to get down to 3.5 MHz. Real-world results will be within ±5% of calculated due to component tolerances. The signal should be stable — not drifting more than a few kilohertz once the circuit is warmed up (2–5 minutes). If using a 100 Ω resistor and oscilloscope probe, you should see a reasonable sine wave at the output, possibly with some clipping on the peaks which is normal for this simple topology.
Frequently Asked Questions
Why are there two capacitors instead of just one in the Colpitts?
The two capacitors serve two roles simultaneously. Together in series they set the resonant frequency of the tank, just as a single capacitor would. But the junction between them also creates a voltage divider that provides the feedback signal to the transistor emitter. A single capacitor could only do one of these jobs. The Colpitts design is elegant because the frequency-setting and feedback functions are combined in the same two components.
What happens if I make C1 and C2 equal?
If C1 = C2, the feedback fraction is 50% — half the tank voltage is returned to the emitter. This is very strong feedback and will cause hard clipping unless the transistor gain is very low. Most practical Colpitts oscillators use C1 much larger than C2 (ratio 3:1 to 10:1) to reduce the feedback to a manageable level (10%–30%) that allows stable, relatively low-distortion oscillation without requiring extremely low transistor gain.
Can I use a FET instead of a bipolar transistor in a Colpitts?
Yes, JFETs and MOSFETs work very well in Colpitts oscillators, often better than bipolar transistors for VFO applications. A JFET (such as the 2N4416, MPF102, or J310) in common-gate configuration draws very little current from the tank (high input impedance), which improves the tank Q and reduces the transistor's capacitances loading the tank. FET Colpitts VFOs typically show lower drift and better frequency stability than bipolar versions for this reason.
How do I tune a Colpitts VFO over a frequency range?
Add a variable capacitor (or varactor diode) in series with the inductor to change the resonant frequency. For a mechanical VFO, a high-quality air-variable capacitor (such as a surplus broadcast receiver tuning capacitor) gives excellent stability and noise-free tuning. For electronic tuning, a reverse-biased varactor diode whose capacitance varies with bias voltage can be placed in series with the tank inductor. Apply a control voltage through an RF choke to avoid loading the tank at RF. Varactors are used in PLL synthesizers to tune the VCO over the required frequency range.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.