must provide the other 180°. Since each capacitor can provide a maximum of 90° of phase shift, RC oscillators require at least two frequency-determining capacitors in the circuit (two poles), and most have three or more, with a comparable number of resistors. This makes tuning the circuit to different frequencies more difficult than in other types such as the LC oscillator, in which the frequency is determined by a single LC circuit so only one element must be varied. Although the frequency can be varied over a small range by adjusting a single circuit element, to tune an RC oscillator over a wide range two or more resistors or capacitors must be varied in unison, requiring them to be ganged together mechanically on the same shaft. The oscillation frequency is proportional to the inverse of the capacitance or resistance, whereas in an LC oscillator the frequency is proportional to inverse square root of the capacitance or inductance. So a much wider frequency range can be covered by a given variable capacitor in an RC oscillator. For example, a variable capacitor that could be varied over a 9:1 capacitance range will give an RC oscillator a 9:1 frequency range, but in an LC oscillator it will give only a 3:1 range. Some examples of common RC oscillator circuits are listed below: Phase-shift oscillator In the phase-shift oscillator the feedback network is three identical cascaded RC sections. In the simplest design the capacitors and resistors in each section have the same value and . Then at the oscillation frequency each RC section contributes 60° phase shift for a total of 180°. The oscillation frequency is The feedback network has an attenuation of 1/29, so the op-amp must have a gain of 29 to give a loop gain of one for the circuit to oscillate Twin-T oscillator Another common design is the "Twin-T" oscillator as it uses two "T" RC circuits operated in parallel. One circuit is an R-C-R "T" which acts as a low-pass filter. The second circuit is a C-R-C "T" which operates as a high-pass filter. Together, these circuits form a bridge which is tuned at the desired frequency of oscillation. The signal in the C-R-C branch of the Twin-T filter is advanced, in the R-C-R - delayed, so they may cancel one another for frequency if ; if it is connected as a negative feedback to an amplifier, and