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A Wien bridge oscillator is a type of electronic oscillator that generates sine waves. It can generate a large range of frequencies. The oscillator is based on a bridge circuit originally developed by Max Wien in 1891. The bridge comprises four resistors and two capacitors. The oscillator can also be viewed as a positive feedback system combined with a bandpass filter.

The modern circuit is derived from William Hewlett's 1939 Stanford University master's degree thesis. Hewlett figured out how to make the oscillator with a stable output amplitude and low distortion. Hewlett, along with David Packard, co-founded Hewlett-Packard, and Hewlett-Packard's first product was the HP200A, a precision Wien bridge oscillator.

The frequency of oscillation is given by:

${\displaystyle f={\frac {1}{2\pi RC}}}$

Amplitude stabilization

The key to Hewlett's low distortion oscillator is effective amplitude stabilization. The amplitude of electronic oscillators tends to increase until clipping or other gain limitation is reached. This leads to high harmonic distortion, which is often undesirable.

Hewlett used an incandescent bulb as a positive temperature coefficient (PTC) thermistor in the oscillator feedback path to limit the gain. The resistance of light bulbs and similar heating elements increases as their temperature increases. If the oscillation frequency is significantly higher than the thermal time constant of the heating element, the radiated power is proportional to the oscillator power. Since heating elements are close to black body radiators, they follow the Stefan-Boltzmann law. The radiated power is proportional to ${\displaystyle T^{4}}$, so resistance increases at a greater rate than amplitude. If the gain is inversely proportional to the oscillation amplitude, the oscillator gain stage reaches a steady state and operates as a near ideal class A amplifier, achieving very low distortion at the frequency of interest. At lower frequencies the time period of the oscillator approaches the thermal time constant of the thermistor element and the output distortion starts to rise significantly.

Light bulbs have their disadvantages when used as gain control elements in Wien bridge oscillators, most notably a very high sensitivity to vibration due to the bulb's microphonic nature amplitude modulating the oscillator output, and a limitation in high frequency response due to the inductive nature of the coiled filament. Modern Wien bridge oscillators have used other nonlinear elements, such as diodes, thermistors, field effect transistors, or photocells for amplitude stabilization in place of light bulbs. Distortion as low as 0.0003% (3 ppm) can be achieved with modern components unavailable to Hewlett.

Wien bridge oscillators that use thermistors also exhibit "amplitude bounce" when the oscillator frequency is changed. This is due to the low damping factor and long time constant of the crude control loop, and disturbances cause the output amplitude to exhibit a decaying sinusoidal response. This can be used as a rough figure of merit, as the greater the amplitude bounce after a disturbance, the lower the output distortion under steady state conditions.

Wien bridge

Bridge circuits were a common way of measuring component values by comparing them to known values. Often an unknown component would be put in one arm of a bridge, and then the bridge would be nulled by adjusting other arms or changing the frequency of the voltage source. See, for example, the Wheatstone bridge.

The Wien bridge is one of many common bridges. Wien's bridge is used for precison measurement of capacitance in terms of resistance and frequency. It was also used to measure frequency.

The Wien bridge does not require equal values of R or C. At some frequency, the reactance of the series R_C–C_C arm will be an exact multiple of the shunt R_D–C_D arm. If the two R_A and R_B arms are adjusted to the same ratio, then the bridge is balanced.

Analysis

If a voltage source is applied directly to the input of an ideal amplifier with feedback, the input current will be:

${\displaystyle i_{in}={\frac {v_{in}-v_{out}}{Z_{f}}}}$

Where ${\displaystyle v_{in}}$ is the input voltage, ${\displaystyle v_{out}}$ is the output voltage, and ${\displaystyle Z_{f}}$ is the feedback impedance. If the voltage gain of the amplifier is defined as:

${\displaystyle A_{v}={\frac {v_{out}}{v_{in}}}}$

And the input admittance is defined as:

${\displaystyle Y_{i}={\frac {i_{in}}{v_{in}}}}$

Input admittance can be rewritten as:

${\displaystyle Y_{i}={\frac {1-A_{v}}{Z_{f}}}}$

For the Wien bridge, Z_f is given by:

${\displaystyle Z_{f}=R+{\frac {1}{j\omega C}}}$

${\displaystyle Y_{i}={\frac {\left(1-A_{v}\right)\left(\omega ^{2}C^{2}R+j\omega C\right)}{1+\left(\omega CR\right)^{2}}}}$

If ${\displaystyle A_{v}}$ is greater than 1, the input admittance is a negative resistance in parallel with an inductance. The inductance is:

${\displaystyle L_{in}={\frac {\omega ^{2}C^{2}R^{2}+1}{\omega ^{2}C\left(A_{v}-1\right)}}}$

If a capacitor with the same value of C is placed in parallel with the input, the circuit has a natural resonance at:

${\displaystyle \omega ={\frac {1}{\sqrt {L_{in}C}}}}$

Substituting and solving for inductance yields:

${\displaystyle L_{in}={\frac {R^{2}C}{A_{v}-2}}}$

If ${\displaystyle A_{v}}$ is chosen to be 3:

${\displaystyle L_{in}=R^{2}C}$

Substituting this value yields:

${\displaystyle \omega ={\frac {1}{RC}}}$

Or:

${\displaystyle f={\frac {1}{2\pi RC}}}$

Similarly, the input resistance at the frequency above is:

${\displaystyle R_{in}={\frac {-2R}{A_{v}-1}}}$

For ${\displaystyle A_{v}}$ = 3:

${\displaystyle R_{in}=-R}$

If a resistor is placed in parallel with the amplifier input, it will cancel some of the negative resistance. If the net resistance is negative, amplitude will grow until clipping occurs. Similarly, if the net resistance is positive, oscillation amplitude will decay. If a resistance is added in parallel with exactly the value of R, the net resistance will be infinite and the circuit can sustain stable oscillation at any amplitude allowed by the amplifier.

Notice that increasing the gain makes the net resistance more negative, which increases amplitude. If gain is reduced to exactly 3 when a suitable amplitude is reached, stable, low distortion oscillations will result. Amplitude stabilization circuits typically increase gain until a suitable output amplitude is reached. As long as R, C, and the amplifier are linear, distortion will be minimal.

An alternative approach, with particular reference to frequency stability and selectivity, will be found in Strauss (1970, p. 671) and Hamilton (2003, p. 449).

See also

• Armstrong oscillator
• Clapp oscillator
• Colpitts oscillator
• Hartley oscillator
• Relaxation Oscillator
• Vačkář oscillator

References

1. Williams (1990, pp. 32–33)
2. Terman 1943, p. 904
3. Terman 1943, p. 904 citing Ferguson & Bartlett 1928

• Ferguson, B. W.; Bartlett (July 1928), "The Measurement of Capacitance in Terms of Resistance and Frequency", Bell System Technical Journal, 7: 420
• Hamilton, Scott (2003), An Analog Electronics Companion: basic circuit design for engineers and scientists, Cambridge University Press, ISBN 9780521798389
• Hamilton, Scott (2007), An Analog Electronics Companion: basic circuit design for engineers and scientists and introduction to SPICE simulation, Cambridge University Press, ISBN 9780521687805
• Variable Frequency Oscillation Generator {{citation}}: Unknown parameter |country-code= ignored (help); Unknown parameter |inventor-first= ignored (help); Unknown parameter |inventor-last= ignored (help); Unknown parameter |issue-date= ignored (help); Unknown parameter |patent-number= ignored (help)
• Oliver, Bernard M. (April–June, 1960), "The Effect of μ-Circuit Non-Linearity on the Amplitude Stability of RC Oscillators" (PDF), Hewlett-Packard Journal, 11 (8–10): 1–7 {{citation}}: Check date values in: |date= (help). Shows that amplifier non-linearity is needed for fast amplitude settling of the Wien bridge oscillator.
• Strauss, Leonard (1970), Wave Generation and Shaping (2nd ed.), McGraw-Hill, ISBN 978-0070621619
• Terman, Frederick (1943), Radio Engineers' Handbook, McGraw-Hill
• Williams, Jim (June 1990), Bridge Circuits: Marrying Gain and Balance, Application Note, vol. 43, Linear Technology Inc, p. 29–33, 43
• Williams, Jim, ed. (1991), Analog Circuit Design, Art, Science, and Personalities, Butterworth Heinemann, ISBN 0750696400

External links

• Model 200A Audio Oscillator, 1939, HP Virtual Museum.
• Circuit Analysis, including SPICE simulation.
• Mancini, Ron; Palmer, Richard (March 2001), Sine-Wave Oscillator (PDF), Application Report, vol. SLOA060, Texas Instruments

• Oscillators
• Analog circuits
• Electronic test equipment
• Electronic circuits