Twin-T Oscillators are another type of RC oscillator which produces a sinewave output for use in fixed-frequency applications similar to the Wein-bridge oscillator. The twin-T oscillator uses two “Tee” shaped RC networks in its feedback loop (hence the name) between the output and input of an inverting amplifier.
As we have seen, an oscillator is basically an amplifier with positive feedback which has a fixed amount of voltage gain required to maintain oscillations, and the twin-T oscillator is no different. Feedback is provided by the twin-T configured RC network allowing some of the output signal to be fed back to the amplifier’s input terminal. Thus the twin-T RC network provides the 180o phase-shift and the amplifier providing another 180o of phase-shift. These two conditions create 360o in total of phase-shift allowing for sustained oscillations.
Unlike the typical RC Phase-shift Oscillator which configures the feedback resistors and capacitors into a ladder network, or the standard Wien-bridge Oscillator which uses the resistors and capacitors in a bridge configuration, the twin-T oscillator (sometimes known as a parallel-T oscillator) uses a passive resistance-capacitance (RC) network with two interconnected “T” sections (having their R and C elements in opposite formation) connected together in parallel as shown.
Clearly we can see that one of the RC passive networks has a low-pass response, while the other has a high-pass response and we have seen this RC network arrangement before in our tutorial about the Notch Filter. The difference this time is that we are using the combined parallel RC T-configured networks to produce a notch type response which has a center frequency ƒc equal to the desired null frequency of oscillation.
The result is that oscillations cannot occur at frequencies above or below the tuned notch frequency due to the negative feedback path created through the twin-T network. However, at the tuned frequency any negative feedback becomes negligible, thus allowing the positive feedback path created by the amplifying device to dominate creating oscillations at one single frequency (unlike the Wien bridge oscillator which can be adjusted over a large frequency range).
Then the twin-T oscillator’s frequency selective twin-T network produces an output transfer function were the frequency, depth and phase-shift of the notch is determined by the component values used. Thus the individual twin-T networks which make up the RC network are defined by the following equations:
For the low-pass R-C-R network:
For the high-pass C-R-C network:
Combining these two sets of equations together will give us the final equation for the null or centre frequency of the notch resulting in oscillations for a twin-T network.
- ƒC is the frequency of oscillations in Hertz
- R is the feedback resistance in Ohms
- C is the feddback capacitance in Farads
- π (pi) is a constant with a value of about 3.142
Having determined the twin-T network for the oscillator that produces the required 180o of phase shift, which occurs at the null frequency between -90o to +90o (as opposed to the zero to 180o for the Wien-bridge oscillator), we need an amplifier circuit to provide the voltage gain. Twin-T oscillator cicruits are best implimented by combining the RC feedback network with an operational amplifier, as due to their high input impedance caharacteristics, op-amps tend to work better with this type of oscillator compared to transistors.
Standard operational amplifiers can provide high voltage gain, a high input impedance as well as a low output impedance and are therefore excellent amplifiers for twin-T oscillators. At the oscillating frequency, ƒc the feedback gain drops to almost zero so we require an amplifier with a voltage gain much greater than one (unity).
The positive feedback required for oscillation is provided by the feedback resistor R1 while resistor R2 ensures start-up. As a general rule of thumb, to ensure that the circuit oscillates as close to the required frequency as possible, the ratio of these two resistors needs to be greater than one-hundred (>100).
To obtain the required positive gain at the oscillating fequency, we can use a non-inverting amplifier configuration where a small part of the output voltage signal is applied directly to the non-inverting ( + ) input terminal via a suitable voltage divider network. The negative feedback produce by the twin-T osccilator circuit is connected to the inverting ( – ) input terminal. This closed-loop configuration produces a non-inverting oscillator circuit with very good stability, a very high input impedance, and low output impedance as shown.
Twin-T Oscillator Circuit
Then we can see that the twin-T oscillator receives its positive feedback to the non-inverting input through the voltage divider network and its negative feedback through the twin-T RC network. To ensure that the circuit oscillates at the required single frequency, the “Tee-leg” resistor R/2 can be an adustable trimmer potentiometer, but can also be adjusted to compensate for capacitor tolerances so that the circuit oscillates at start-up.
Twin-T Oscillator Example No1
A twin-T oscillator circuit is required to produce a 1kHz sinusoidal output signal for use in an electronic circuit. If an operational amplifier with a gain ratio of 200 is used, calculate the values of the frequency determining components R and C, and the values of the gain resistors.
The frequency of oscillation is to be 1kHz, if we select a reasonable value for the two feedback resistors, R of 10kΩ (remember that these two resistors must have identical values) we can calculate the value of capacitor required using the formula for the frequency of oscillations from above.
Thus R = 10kΩ, and C = 16nF. The center Tee-leg capacitor 2C = 2 x 16nF = 32nF, so the nearest preferred value of 33nF is used.
As the value of the high-pass branch tee-capacitor is 33nF and therefore not exactly equal to 2C (2 x 16nF), we can adjust for this variation and ensure the correct start-up of oscillations by adjusting the low-pass branch tee-resistor by the same amount. Thus the exact value of R(leg) would be 10kΩ/2 = 5kΩ, but the calculated value of this resistor is given as: R(leg) = R/(33nF/16nF) = 4.85kΩ. Clearly then the use of a 5kΩ trim-pot would meet our requirements in this example.
The loop gain of the operation amplifier is required to be 200, so if we choose a value of 1kΩ for R2 then resistor R1 will be 200kΩ as shown.
Final Twin-T Oscillator Circuit
Twin-T Oscillator Circuit Summary
We have seen in this tutorial that Twin-T Oscillator Circuits can easily be constructed using some passive components and an operational amplifier. The twin-T oscillator circuit uses a tuned RC network for the feedback circuit to produce the required sinusoidal output waveform. Being two T-networks connected together in parallel, they operate in anti-phase to each other creating zero output at the null frequency, but a finite output at all other frequencies.
As a result, the circuit will not oscillate at frequencies above or below the tuned frequency due to the negative feedback through the twin-T RC network. Therefore at the null frequency, the voltage at the non-inverting input of the op-amp is in phase with its output voltage, giving rise to continuous oscillations at the desired frequency.
To ensure that the oscillation frequency is close to the null frequency as possible, a trim-pot can be used in the tee-leg resistor of the low-pass stage to balance the RC network for start up and purity of output waveform as one of the major disadvantage of the “twin-T oscillator” is that the oscillation frequency and quality of the output waveform is much dependent on the interaction of the resistors and capacitors in the twin-T network then clearly the values and selection of these components must be accurate to ensure oscillation at the desired null frequency.