frequency at which the total phase shift of each branch of the bridge will be equal. If Rb / Rf has no phase shift and the phase shifts of the amplifiers inputs are zero then the bridge is balanced when: and where ω is the radian frequency. If one chooses R1 = R2 and C1 = C2 then Rf = 2 Rb. In practice, the values of R and C will never be exactly equal, but the equations above show that for fixed values in the Z1 and Z2 impedances, the bridge will balance at some ω and some ratio of Rb/Rf. Analysis Analyzed from loop gain According to Schilling, the loop gain of the Wien bridge oscillator, under the condition that R1=R2=R and C1=C2=C, is given by where is the frequency-dependent gain of the op-amp (note, the component names in Schilling have been replaced with the component names in the first figure). Schilling further says that the condition of oscillation is T=1 which, is satisfied by and with Another analysis, with particular reference to frequency stability and selectivity, is in and . Frequency determining network Let R=R1=R2 and C=C1=C2 Normalize to CR=1. Thus the frequency determining network has a zero at 0 and poles at or −2.6180 and −0.38197. Amplitude stabilization The key to the Wien bridge oscillator's low distortion oscillation is an amplitude stabilization method that does not use clipping. The idea of using a lamp in a bridge configuration for amplitude stabilization was published by Meacham in 1938. 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 power detector, low pass filter and gain control element in the oscillator feedback path to control the output amplitude. The resistance of the light bulb filament (see resistivity article) increases as its temperature increases. The temperature of the filament depends on the power dissipated in the filament and some other factors. If the oscillator's period (an inverse of its frequency) is significantly shorter than the thermal time constant of the filament, then the temperature of the filament will be substantially constant over a cycle. The filament resistance will then determine the amplitude of the output signal. If the amplitude increases, the filament heats up and its resistance increases. The circuit is designed so that a larger