# Analysis of a Digitally Controlled Wien-Bridge Oscillator

Abstract: Of all the low-frequency oscillator configurations, the Wien bridge is the easiest to use. It is reliable, uses standard components, gives a good sine wave, and is fairly immune to the type of op amp around which it is designed. A Wien bridge can, however, be misunderstood and oversimplified, leading to designer frustration. This article describes the theory and practicalities of using a Wien-bridge oscillator, and how to make the circuit more stable and more factory-/user-flexible.

## The Wien-Bridge Oscillator Circuit

**Figure 1**.

*Figure 1. A standard Wien-bridge oscillator circuit.*

(Eq. 1) |

(Eq. 2) |

(Eq. 3) |

(Eq. 4) |

**Figure 2**shows a simple spreadsheet illustrating the values of the Wien-bridge network and their impact on the gain. Cell B7 is the transfer function represented in Equation 3, cell B12 is determined in Equation 2 (with the answer in kHz), and cell B9 is the reciprocal of cell B7. If C1 = C2 = 10nF and R1 = R2 = 10kΩ, the circuit oscillates at 1.59kHz with an op amp gain equal to 3. A practical measurement of this circuit supports this calculation.

*Figure 2. Example of Wien-bridge component values.*

*just*biased to the point of oscillation. Any less gain and the circuit stops oscillating; any more gain and it starts to distort.

**Figure 3**, solves this problem. With the JFET, the gain can vary over a small range to ensure consistent oscillation. At startup, the JFET gate voltage is zero; therefore, the drain-source impedance is very low. This design produces a gain greater than 3 (to get the circuit going). Once oscillations build up, the rectified negative transitions of the output provide a turn-off voltage for the JFET's gate. This reduces the gain, and the circuit settles down to stable oscillation. The amplitude of the output depends on the voltage drop across the two diodes, as well as the turn-off voltage of the JFET. Unfortunately, JFETs have a large variation in gate turn-off voltage, which causes the circuit's output voltage to vary considerably from batch to batch. TR1 was selected because it has a very low variation of gate turn-off voltage, thus guaranteeing a small variation in output voltage from circuit to circuit. But this TR1 circuit often does not yield the lowest distortion oscillator. In fact, the circuit oscillates, but with significant distortion; the JFET maintains this oscillation regardless of the distortion. Therefore, the JFET should only be used as an aid to keep the circuit going, not to compensate for poor circuit design.

*Figure 3. A Wien-bridge oscillator with a junction gate field-effect transistor (JFET) in the feedback network.*

**Figure 4**shows the final circuit including the MAX5467 digipot.

**Figure 5**shows an AC ground and a JEFT bias circuit.

**Figures 6**and

**7**show frequency- and gain-adjust circuits, respectively. The digipots are represented by the symbols IC2, IC3, and IC4. IC2 and IC3 share the same digital interface and, hence, can be incremented and decremented simultaneously. IC4 provides an independent gain-adjust circuit.

*Figure 4. A Wien-bridge oscillator with a JFET and a digipot in the feedback network.*

*Figure 5. An AC ground and a JFET bias circuit.*

*Figure 6. A frequency-adjust circuit using the MAX5467.*

*Figure 7. A gain-adjust circuit using the MAX5467.*