Simulating a Colpitts Oscillator in LTspice

From Resonance to Oscillation: The Barkhausen Criterion

An LC tank circuit, when "plucked" with a bit of energy, will ring at its resonant frequency, but these oscillations quickly die out due to inherent resistance. Think of it like striking a bell; the sound fades away. To create a continuous tone, we need to continuously add back the energy that is lost in each cycle.

In electronics, we achieve this using an amplifier and a feedback loop. The amplifier takes the small, decaying oscillation from the tank, boosts its power, and feeds a portion of that amplified signal back into the tank at just the right moment to reinforce the oscillation.

The conditions required for this to work are formally known as the Barkhausen Stability Criterion. For a self-sustaining, stable oscillation to occur, two conditions must be met at the desired frequency of oscillation:

1. Magnitude Condition: The total gain of the amplifier and feedback loop (the "loop gain") must be equal to one. $|A\beta |=1$. In practice, to start the oscillation from random noise, the gain must be slightly greater than one. The oscillation then grows until circuit non-linearities effectively reduce the gain back to one, stabilizing the amplitude.
2. Phase Condition: The total phase shift around the feedback loop must be exactly 0° or a multiple of 360°. This ensures the feedback signal is "in phase" with the original oscillation, reinforcing it rather than canceling it out.

The following video provides an excellent derivation of these conditions for a general LC oscillator.

The Colpitts Oscillator Topology

There are several ways to arrange the amplifier and feedback network. One of the most common and practical designs is the Colpitts oscillator. Its defining feature is a tank circuit that uses a single inductor (L) and a capacitive voltage divider (two capacitors, C1 and C2, in series) to provide the feedback signal.

Let's see how the general oscillation conditions apply specifically to this circuit.

These two formulas are our design equations. They tell us how to choose component values to get the frequency we want and the gain we need to sustain oscillation.

Simulating the Colpitts Oscillator in LTspice

Now, let's apply this theory and build a Colpitts oscillator in LTspice that operates at approximately 1 MHz, which falls within the AM broadcast band. This will be useful later when we build the physical circuit. We'll follow the design choices discussed in the video you just watched.

1. Create a New Schematic and Place Components

Open LTspice and start a new schematic. We will build the circuit shown in the diagram above.

• Transistor (Q1): The choice of transistor is important for RF circuits. A general-purpose transistor might not have a high enough transition frequency ($f_T$) to operate at 1 MHz. We will use a BC547C, which is a common NPN BJT that works well for this application. Press F2 and type BC547C to find it.
• Resistors (R1, R2, RC, RE): These form the biasing network to set the transistor's DC operating point (the Q-point), ensuring it acts as an amplifier.
• Capacitors (C1, C2, C_in, C_out, C_E): C1 and C2 form the tank circuit's capacitive divider. The others are DC-blocking or bypass capacitors.
• Inductor (L1): The inductor for our tank circuit.
• Voltage Source (V1): Our DC power supply.

2. Set Component Values

Right-click on each component to set its value according to our 1 MHz design target:

• Power Supply: V1 = 9V
• Biasing Network: R1=12k, R2=8.8k, RC=1k, RE=1k
• Tank Circuit:
  • C1 = 1n (1 nanofarad)
  • C2 = 1n (1 nanofarad)
  • L1 = 50u (50 microhenries). The video calculated 50.66µH; 50µH is a standard value and will get us very close.
• Coupling/Bypass Capacitors: C_in=82n, C_out=82n, C_E=10u

Your schematic should look similar to the one in the video LTSPICE 1 GHz RF Colptits Oscillator. The following clip provides a helpful visual guide for constructing the circuit, although it uses different component values for a higher frequency. The overall structure is the same.

3. Set up the Simulation Command

Unlike our last lesson, we are not sweeping frequencies. We want to see the circuit's voltage over time to observe the oscillation. This requires a Transient Analysis.

1. Go to Simulate -> Edit Simulation Command.
2. Select the Transient tab.
3. Set the Stop Time. A value of 200u (200 microseconds) will be enough to see many cycles of our ~1 MHz wave.
4. To ensure the simulation starts cleanly and captures the initial build-up of oscillations from numerical noise, check the box that says "Skip initial operating point solution".
5. Click OK and place the .tran 0 200u 0 startup directive on your schematic.

4. Run the Simulation and Analyze the Output

Click the "Run" button. When the plot window appears, probe the wire at the collector of the transistor (Q1), which is our output node.

You should see a beautiful sine wave! It will likely start at zero, rapidly grow in amplitude, and then stabilize. This is your oscillator in action.

• Verify the Frequency: Use the cursors to measure the time period (T) of one full cycle of the wave. The frequency is $f=1/T$. Does it match our target of ~1 MHz?
  • With L=50µH and C_eq = (1nF * 1nF) / (1nF + 1nF) = 0.5nF, the calculated frequency is $f_r=\frac{1}{2\pi \sqrt{50\times 10^{-6}\cdot 0.5\times 10^{-9}}}\approx 1.007\text{ MHz}$. Your simulation should be very close to this.
• Observe the Amplitude: Notice how the wave's amplitude is limited by the power supply. It cannot go above 9V or below 0V. The stabilization of the amplitude is due to the transistor's non-linear behavior, just as discussed in the theory video.

As a final experiment, you can try changing the transistor from BC547C to the generic NPN transistor in LTspice. As the LINK video demonstrates, the choice of active device is critical, and a less capable transistor may fail to sustain oscillations at this frequency.

Conclusion

In this lesson, you have taken a significant step from analyzing passive circuits to designing an active one. You have successfully simulated a functional RF oscillator, the fundamental building block of a transmitter.

Here are the main takeaways:

• An oscillator combines a resonant tank with an amplifier and a feedback loop to sustain continuous oscillation.
• The Barkhausen Criterion defines the necessary gain ($|A\beta |\ge 1$) and phase ($\angle A\beta =0^{\circ }$) conditions for oscillation.
• The Colpitts oscillator is a specific topology that uses a capacitive divider in its LC tank to create the feedback signal.
• You used a Transient (.tran) analysis in LTspice to observe the oscillator's output waveform over time, verifying its frequency and amplitude.

You are now well-prepared for the next lesson, where we will move from the virtual world to the physical one. We will take the exact circuit you just designed and build it on a breadboard.