# Wien Bridge Oscillator Construction and Performance

## The beauty and performance of classic circuits

The Wien Bridge oscillator is a classic circuit that everyone should build. It is an elegant circuit providing a remarkably low-distortion sinusoidal waveform. It provides valuable lessons in filtering, feedback, and automatic gain control. Surprisingly, the heart of the circuit is an incandescent light bulb that stabilizes the gain of the circuit.

The type 7374 incandescent lamp can be seen in Figure 1 to the left of the LF412 operational amplifier. Use of a simple incandescent lamp is desirable as the lamp’s resistance changes with self-heating temperature. It is low when the bulb is cold and increases as the bulb heats up. This property is reflected in Figure 2. Here we see that the cold (1 VDC) resistance is about 125 Ω. When the lamp voltage reaches its rated 28 VDC, the filament resistance has increased to about 700 Ω. This is a non-linear resistance change with a positive temperature coefficient.

Figure 1: Picture of the prototype Wien Bridge Oscillator featuring a type 7374 lamp and an LF412 op amp.

Tech Tip: No introduction to the Wien bridge oscillator would be complete without mentioning the Hewlett-Packard HP 200A audio oscillator. This vacuum tube circuitry featured a similar light bulb to stabilize the amplifier’s gain. The oscillator used a large air-variable capacitor to adjust the output frequency. For more information about this classic piece of test equipment please see:

Figure 2: Nonlinear resistance curve for the 7374 incandescent lamp.

## Maintain gain stability using an incandescent lamp

The schematic for the Wien bridge oscillator is included as Figure 3. Note that the 7374 light bulb is associated with the op amp’s inverting input. Recall that the gain of an op amp is determined by the ratio of the feedback to input resistance:

Gain \propto \dfrac{R_f}{R_{In}}

In Figure 3 we see that the lamp has taken the place of R_{In}. Consequently, the gain of the circuit is tied to the lamp’s resistance:

Gain \propto \dfrac{R_f}{R_{lamp}}

As the output of the oscillator increases, it will increase the heat in the lamp. This increase in heat causes a corresponding increase in resistance. This increased resistance tends to lower the gain of the system. Taken together, this provides a natural feedback mechanism that keeps the oscillator’s output constant.

Figure 3: Schematic of the Wien Bridge Oscillator featuring the type 7374 lamp and an LF412 op amp.

## Component Values for the typical Wien bridge oscillator

The classic equations governing the circuit are:

f = \dfrac{1}{2 \pi R_1C_1}

and

R_f = 2R_b

Rather than show the derivation, let’s explore a practical method for determining the component values. Let’s start with R_f. Knowing that R_f = 2R_b, we can use a voltage divider to calculate the lamp voltage in terms of the output voltage.

V_b = V_{Out}\dfrac{R_b}{R_b + R_f} = V_{Out}\dfrac{R_b}{R_b + 2R_b} = \dfrac{1}{3}V_{Out}

Knowing this property, we can, within limits, select an R_f for our desired output voltage. For example, suppose we have +/- 12 VDC rails and desire a +/- 6 volt peak output. The resulting RMS output voltage is 4.2 V. Using our equations, we see that 1/3 or 1.4 V is applied across the lamp. Using the Figure 2 table, this corresponds to a 150 Ω (hot bulb resistance). We can then select the R_f as 2R_b or about 300 Ω.

As for R1 and C1, suppose we desire a 1 kHz output signal. As typically done, we first select a capacitor and then the appropriate resistors. If we let C_1 = 0.1 uF, a resistor of 1.6 kΩ is appropriate for R_1.

You may or may not want to trim the resistors to center the amplifier at 1 kHz. It is also possible to add dual-ganged resistor or a dual-ganged capacitors to provide a variable frequency output. Resistors are relatively easy to source while large variable capacitor are expensive and largely a thing of the past except for specialized RF applications.

Tech Tip: It is often convenient to start with the capacitor value for oscillator and filter circuits. This reflects component availability. It’s a recognition that there are considerably more discrete resistor values than there are capacitor values.

## Performance of the Wien bridge oscillator

The circuit performance was measured using a Digilent Analog Discovery 3. The circuit was powered by +/- 12 VDC rails. The resulting Figure 4 oscilloscope view shows a clean sinusoid with an amplitude of approximately +/- 6 Volts. The frequency is approximately 1 kHz.

Figure 5 provides support for the low-distortion claim. Here we see the 1 kHz spike. There are no measurable harmonics in the -80 dBm noise floor. This is remarkable performance for such as simple circuit.

Figure 4: The Wien bridge oscillator produces a +/- 6 VDC signal at approximately 1 kHz.

Figure 5: The spectrum of the Wien bridge oscillator is pure with no measurable harmonics -80 dBm below the peak.

Tech Tip: The Wien bridge oscillator operates with a wide range of resistors. This is not surprising as the Figure 2 curve shows the lamp has a positive temperature coefficient all the way up to its maximum operating voltage. The limiting factor is the op amp’s design-maximum rail voltage. For low distortion, we must avoid clipping by limiting the output to about ½ of the rail voltage. In this article the peak oscillator output was limited to ½ the rail voltage.

## Applications of the Wien bridge oscillator

Adding a low-cost quality oscillator to your test bench is desirable. One useful application is testing the distortion of an amplifier. Here we send the clean sinusoid into the amplifier and then look for harmonics. The advent of low-cost spectrum analyzers such as the Digilent Analog Discovery featured in this article provides an easy way to see these harmonics. As an experiment, you could construct a simple common-base transistor amplifier and see how it responds to changes such as bias, degenerative emitter resistance, rail voltage, and temperature.