# Application Note AN45

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1 Application Note Wien Bridge Oscillators using E 2 POTs by Applications Staff, October 1994 Wien Bridge Oscillators In 1939, William R. Hewlett (later of Hewlett-Packard fame) first combined the network described by Wien in 1891 with a gain stabilizing element in a bridge configuration, to produce an oscillator based on a 6J7 vacuum tube. Few circuit designs can match the low distortion, good amplitude stability, ease of tuning, and circuit simplicity offered by the Wien bridge oscillator. The Wien bridge oscillator is based upon an amplifier with two feedback paths, making up the two arms of the bridge. One arm of the bridge is the Wien network, which provides the frequency tuning elements, and another arm which establishes amplitude equilibrium. Figure 1 shows the configuration using an Operational Amplifier. Positive feedback is provided by the Wien network comprised of equal-valued C1, R1, C2, and R2 elements. Negative feedback is provided by R3 and R4. To understand how the Wien bridge oscillator works, assume that at power-up, the negative feedback is made less than the positive feedback. Oscillation will start to occur at the frequency where the phase shift and amplitude attenuation in the Wien arm is a minimum. Figure 2 shows the response functions for magnitude and phase from the amplifier output to the noninverting (+) input with C=.1µF and R=1KΩ. Notice that when the phase equals zero degrees, the magnitude of the positive feedback is a maximum and equal to 1/3. The oscillator amplitude will continue to increase until the amplifier saturates (and produces horrible square waves) or until amplitude equilibrium is maintained below saturation by adjusting the ratio of R3 and R4. Hewlett did this by taking advantage of the positive temperature coefficient of an incandescent lamp. It is interesting to note that when equilibrium is reached, the negative feedback factor will also be 1/3 (in a practical circuit, due to non-ideal components, the negative feedback will be slightly less). C R C1 R1 1 ƒ = 2πRC + R3 R R2 C2 C 2R-feedback R4 R-feedback Figure 1. Wien Bridge Oscillator /24/95 TD Xicor, Inc Buckeye Drive Milpitas, CA 9535 (48)

2 A Wien bridge Oscillator with E 2 POTs Notice that to change frequency, it is necessary to either change both Rs or both Cs of the network and that the Rs or Cs have to change by the same amount or track each other. Hewlett accomplished this by using a pair of ganged air-variable capacitors mechanically linked to a tuning knob. You could get similar results by using a pair of ganged potentiometers instead. However, ganged variable capacitors and resistors are rather bulky and expensive mechanical items that require manual adjustment to change frequency. Since a pair of Xicor E 2 POTs can be electronically ganged together, they can provide a solid state solution and eliminate the need for any mechanical mounting considerations involved with the airvariable capacitors or the ganged mechanical pots. The benefit of using these digital pots is that the control circuitry can be located remotely from the actual oscillator since the pots are controlled digitally, you don t have to worry about the frequency being inadvertently bumped out of adjustment. Circuit description Figure 3 shows the Xicor X9C13 E 2 POT in a Wien bridge circuit along with remote pushbutton control Bridge Network Phase circuitry. The frequency is determined by the combination of C1, C2, R1+U1, and R2+U2. Assuming that C1=C2 and R1+U1=R2+U2, the frequency is: f= 1 (2 C1(R1+ U1)) π The negative feedback is set by the combination of R3, R4A, R4B, and Q1. Q1 in parallel with R4B, plus R4A, forms the shunt elements in the negative feedback path. The channel resistance of Q1 is controlled by the amplitude detector circuit comprised of CR3, U3B, R11, and C7. U3B compares the positive peaks of the oscillator output detected by CR3, to the voltage reference established by R11 and R12. The amplitude detector scheme automatically sets the negative feedback so that the peak output just equals the reference voltage. This limits the oscillator voltage swing so that U3A does not saturate and maintains the amplitude equilibrium, which is important when generating sine waves. To ensure that cycle by cycle limiting is not occurring, the time constant of R11 and C7 is much longer than the lowest frequency which the oscillator can be tuned Bridge Network Magnitude Hz Hz Figure 2. Bridge Network Phase and Magnitude /24/95 TD -2

3 Figure 3. Xicor X9C13 Wien Bridge /24/95 TD -3

4 Beyond the fact that equal valued Rs and Cs must be used in the Wien arm of the oscillator, there is nothing critical about the components used. Any Op Amp can be used as long as the input or output common mode voltage ranges are not exceeded. The FET can be most any N-channel device as long as R11 and C7 are optimized to keep the gain control loop stable. This circuit design can be modified to suit just about any application. For example, you may wish to add an additional Xicor E 2 POT in place of R13 in order to control the output amplitude. You could also implement digital range selection by using a MOSFET switch to select alternate values of C1 and C2 in decade increments. This should allow selection of decade ranges of 2Hz to 2Hz, 2Hz to 2KHz, 2KHz to 2KHz, and 2KHz to 2KHz. Performance Naturally, for the oscillator to work properly, the two digital pots have to be initially ganged together. This is accomplished simply by holding either of the controller pushbuttons down for at least 1 steps. After this procedure is performed, the pots will always track and the frequency can be set as desired. Figure 4 shows the output frequency verses step number. With the values used in the schematic the frequency range should be approximately 2KHz to 2KHz in 1 steps. The output amplitude is 2.2V RMS. The total distortion and noise of this circuit was measured to be approximately.5% and most of the distortion products are second harmonics. This second harmonic is caused by the channel resistance of the gain control FET, Q1, being modulated by the oscillator frequency. You can further reduce the distortion by adding a small amount of Q1 drain signal onto the gate with an appropriate resistor divider network. The amplitude stability of this oscillator is excellent with no change in output being perceptible over the full range. No doubt, this is why these oscillators proved to be so useful in test application. Remember, one of the advantages of the E 2 POTs is their nonvolatility, so the frequency will always be maintained, even if the oscillator and controller is powered-down. In fact, after the frequency is set, the controller can be removed. This circuit could prove useful in embedded built-in test equipment (BTE) applications where it is desirable to have a programmable oscillator with low distortion and good amplitude stability /24/95 TD -4

5 Frequency vs Step No Step No. Figure 4. Oscillator Tuning /24/95 TD -5

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