Simple Single-BJT Colpitts Oscillator – LC Sine Wave Generator

An LC oscillator, like the Colpitts oscillator, is a simple way to make a sine wave. It uses just an inductor and a capacitor, sometimes called a tank circuit, where energy moves back and forth between the two. At the right frequency, this creates a smooth sinusoidal signal. But in practice, the oscillation quickly dies out because real components always lose some energy.

To keep the sine wave going, the circuit needs a transistor amplifier and a small amount of feedback. A Colpitts oscillator does this in a very simple way by using one inductor and two capacitors. In this article, we’ll first look at how a basic LC tank works, then step up to a single-transistor Colpitts oscillator that produces a steady sine wave using only a few parts.

What’s an LC or Tuned Circuit?

In its most basic form, an LC circuit—also known as a tuned circuit, tank circuit, or sometimes resonant circuit—consists of an inductor (L) and a capacitor (C). Like how a musical tuning fork always resonates at the same frequency when hit, each LC circuit has a resonating frequency that’s determined by the inductor and capacitor. 

To see the LC circuit resonating frequency in action, let’s assume a circuit with one inductor (L) and a capacitor (C) connected in a closed loop. Now, suppose that the capacitor is fully charged, i.e., it holds maximum potential energy in its electric field.

The moment the time starts, current begins to discharge from the capacitor through the inductor, generating a magnetic field around the coil. This process basically converts electric potential energy on the capacitor’s plates into magnetic potential energy around the coil.

After the current in the circuit reached its maximum and the capacitor completely depleted its charge, the magnetic field began to collapse. And according to Lenz’s law, as the magnetic field contracts, it induces current in the same direction, attempting to maintain its shape. This action directs current to recharge the capacitor again, but now in the opposite polarity.

Once the magnetic field is exhausted and the capacitor plates hold opposite charges relative to the starting condition, the capacitor begins to discharge, and the cycle repeats in the opposite direction. 

The cycle continues, and the capacitor switches back and forth between positive and negative, creating an oscillation. The speed of this oscillation is called a resonating frequency, which, as mentioned before, is determined by L and C.

However, the oscillation cannot continue forever. Just like a pendulum that stops due to friction, an LC circuit loses some of its magnitude each cycle through internal resistances and power dissipation. Eventually, it reaches a stable equilibrium where there is no current flow (ideally).

Real-World Effects

In practice, we can briefly examine this process by assembling an LC network with an inductor and a capacitor. Then, use a power source or battery and a switch to charge it. When the switch is on, current goes to charge both the inductor and the capacitor. 

When we turn off the switch, the LC network is cut off from the power source, and it begins to oscillate. 

If we use an oscilloscope to read the voltage across the capacitor, we’ll see a wavy or sine wave as shown in the graph. This is because the reactance of both the inductor and the capacitor acts similarly to varying resistance, causing the capacitor voltage to change nonlinearly.

Note: Be careful not to leave the battery connected to the LC circuit for too long. Because current through the inductor can get very high (ideally we would want a resistor in series with the source). Also, the oscillation may be very brief and run out before we can read it.

The Resonant Frequency

The LC network resonant frequency (speed of oscillation) is calculated using the following formula. In a word, the frequency is the inverse of the square root of L times C.

$$f=\frac{1}{2 \pi \sqrt{LC}}$$

Where f is the network’s natural resonant frequency, L is the inductor inductance in henries, and C is the capacitor capacitance in farads. Here is a real-values usage example of the formula. Suppose that L = 22mH and C = 1μF.

$$\begin{align*}L&=22\text{mH} = 0.022\text{H}
C&=1\mu \text{F}=1\times 10^{-6}\text{F}\end{align*}$$

So,

$$\begin{align*}f&=\frac{1}{2 \pi \sqrt{0.022 \times 10^{-6}}}\text{Hz}
&=1073.02 \text{Hz}\end{align*}$$.

Colpitts Oscillator

Since we’ll be discussing the Colpitts transistor oscillator in this article, let’s learn more about the LC oscillator topology. A Colpitts oscillator feedback circuit consists of a tank circuit with two capacitors in parallel and an inductor in between, as shown in the simplified diagram below.

C2 is connected to the inverting amplifier input. On the other hand, the feedback signal from the inverting amplifier enters the LC feedback circuit through C1 before being output to the amplifier via C2, producing a feedback loop. The inverting amplifier we’re using for today’s circuit is a transistor.

In this feedback circuit, the phase across C2 (output) is shifted by 180° (inverted) relative to C1 (input). Another 180° phase shift is produced at the inverting amplifier, shown in Figure 3. Altogether, the total phase shift in the loop adds up to 360°, or no phase shifts, which satisfies the Barkhausen criterion for sustained oscillation.

The Output Frequency

Similar to the LC resonant frequency, the output frequency of the Colpitts oscillator is directly proportional to the inductance and capacitance, as shown by the formula below. 

$$f=\frac{1}{2 \pi \sqrt{LC_{t}}}$$

Where f is the output frequency, and L is the inductance of L1. However, instead of only C1 or C2 capacitance, this formula calls for Ct, the product of C1 and C2 divided by their sum.

$$C_{t}=\frac{C_{1}\times C_{2}}{C_{1}+ C_{2}}$$

This means that C1 and C2 can have different values and that they both contribute equally to the output frequency, allowing for finer adjustments.

Designing Basic Transistor LC Oscillator Circuits

Now that we know the basics of the LC network (tank circuit), let’s put it to good use by designing an oscillator based on that principle. We’ll start with the most basic design we think will work, then continue to improve and fix it based on the problems that will eventually pop up.

First Circuit That Doesn’t Work in the Real World

We first tested this design using circuit simulation software and then optimized it based on the results, yielding the Colpitts oscillator circuit shown below.

This circuit works flawlessly within the simulation software. However, when we tested it using real components, it didn’t work. There was no oscillation at the output. We measured the Q1 voltages, and the result shows Vbe = 0.6V and Vce = 2.34V, so the transistor is indeed working, but the circuit refuses to oscillate. 

This situation clearly meant that there are factors that we haven’t taken into account in the simulation. It also demonstrates the limits of the simulation software. At this point, we tried to tinker with the real circuit, looking for a resistor configuration that sets the most suitable current for the transistor.

Second Working Circuit Based on the First One

Shortly after, we landed at the circuit shown in Figure 6. A couple of changes we made include replacing Rb with a 10kΩ potentiometer, removing Re completely (labeled R3 in Figure 5), and lowering Rc to 1kΩ.  In this configuration, the transistor’s Ic should substantially increase, while Ib should also be the same. Meaning that even if the transistor has a low amplification gain, the circuit should still work.

With VR1 turned to approximately 40% (≈4kΩ), the output shows a sine signal. The sine waveform is relatively good with an almost perfect duty cycle of 49.7%. That said, the frequency is a bit higher than anticipated at 4.162kHz, while the peak-to-peak voltage (Vp-p) is very low at only 217mV. 

The output peak-to-peak voltage can be amplified later if we like. For now, we need as perfect a sine wave as possible, and this circuit already produces one nicely. Regarding the frequency, there’s currently no effective means to adjust it without also affecting the waveform, so we would have to accept it as a system tolerance.

We also test two other versions of this Copitts oscillator idea, as well as one with different LC timing for a higher output frequency. If you’re interested, you can check them out on our Patreon page.

Conclusion

The LC oscillator, particularly in the Colpitts topology, works fairly well even with a basic circuit design. The main issue we have now is that the output peak-to-peak voltage is lower than we would like. However, that can be remedied with additional amplifier stages, which we may take a look at in the future.

Compared to the RC phase-shift oscillator, we’d say that this LC oscillator may have produced a cleaner sine-wave output. That said, if the LC needs an amplifier to take the output to a more usable level, the RC version may still be easier to construct and use.

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