Editing Wien bridge oscillator (section)

===Hewlett's oscillator===
[[File:Wien bridge oscillator schematic from Hewletts US patent.png|thumb|300px|Simplified schematic of a Wien bridge oscillator from Hewlett's US patent 2,268,872.  Unmarked capacitors have enough capacitance to be considered short circuits at signal frequency.  Unmarked resistors are considered to be appropriate values for biasing and loading the vacuum tubes.  Node labels and reference designators in this figure are not the same as used in the patent.  The vacuum tubes indicated in Hewlett's patent were pentodes rather than the triodes shown here.]]

[[William Redington Hewlett|William R. Hewlett]]'s Wien bridge oscillator can be considered as a combination of a differential amplifier and a Wien bridge, connected in a positive feedback loop between the amplifier output and differential inputs. At the oscillating frequency, the bridge is almost balanced and has very small transfer ratio. The [[loop gain]] is a product of the very high amplifier gain and the very low bridge ratio.<ref name="Schilling">{{Harvnb|Schilling|Belove|1968|pp=612–614}}</ref>  In Hewlett's circuit, the amplifier is implemented by two vacuum tubes.  The amplifier's inverting input is the cathode of tube V<sub>1</sub> and the non-inverting input is the control grid of tube V<sub>2</sub>.  To simplify analysis, all the components other than R<sub>1</sub>, R<sub>2</sub>, C<sub>1</sub> and C<sub>2</sub> can be modeled as a non-inverting amplifier with a gain of 1+R<sub>f</sub>/R<sub>b</sub> and with a high input impedance.  R<sub>1</sub>, R<sub>2</sub>, C<sub>1</sub> and C<sub>2</sub> form a [[bandpass filter]] which is connected to provide positive feedback at the frequency of oscillation. R<sub>b</sub> self heats and increases the negative feedback which reduces the amplifier gain until the point is reached that there is just enough gain to sustain sinusoidal oscillation without over driving the amplifier.  If R<sub>1</sub> = R<sub>2</sub> and C<sub>1</sub> = C<sub>2</sub> then at equilibrium R<sub>f</sub>/R<sub>b</sub> = 2 and the amplifier gain is 3. When the circuit is first energized, the lamp is cold and the gain of the circuit is greater than 3 which ensures start up. The dc bias current of vacuum tube V1 also flows through the lamp.  This does not change the principles of the circuit's operation, but it does reduce the amplitude of the output at equilibrium because the bias current provides part of the heating of the lamp.

Hewlett's thesis made the following conclusions:<ref>{{harvnb|Hewlett|1939|p=13}}</ref>
: A resistance-capacity oscillator of the type just described should be well suited for laboratory service.  It has the ease of handling of a beat-frequency oscillator and yet few of its disadvantages.  In the first place the frequency stability at low frequencies is much better than is possible with the beat-frequency type.  There need be no critical placements of parts to insure small temperature changes, nor carefully designed detector circuits to prevent interlocking of oscillators.  As a result of this, the overall weight of the oscillator may be kept at a minimum.  An oscillator of this type, including a 1 watt amplifier and power supply, weighed only 18 pounds, in contrast to 93 pounds for the General Radio beat-frequency oscillator of comparable performance.  The distortion and constancy of output compare favorably with the best beat-frequency oscillators now available.  Lastly, an oscillator of this type can be laid out and constructed on the same basis as a commercial broadcast receiver, but with fewer adjustments to make.  It thus combines quality of performance with cheapness of cost to give an ideal laboratory oscillator.

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