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Module 2:
1.1 Oscillators: An oscillator is basically a signal generator that produces a
sinusoidal or non-sinusoidal signal of some particular frequency. Sometimes, an
oscillator is said to be an amplifier with positive feedback.
Positive feedback:
Figure shows the block diagram of an amplifier stage with positive feedback
applied. Note that the amplifier provides a phase shift of 180° and the feedback
network provides a further 180°. Thus the overall phase shift is 0°. The overall
voltage gain, G, is given by:
Fig: Amplifier with positive feedback applied
Now consider what will happen when the loop gain, β A v, approaches unity (i.e., when the loop gain is just less than 1). The denominator (1 - β A v) will become close to zero. This will have the effect of increasing the overall gain, i.e. the overall gain with positive feedback applied will be greater than the gain without feedback.
1.2 Conditions for oscillation ( Barkhausen's criteria for oscillation )
Oscillator is a device that generates continuous and periodic waveforms without taking input signal.The conditions for oscillation are: (a) the feedback must be positive (i.e. the phase shift must be 0o^ or 360 o.); (b) the overall loop voltage gain must be greater than 1 (i.e. the amplifier’s gain must be sufficient to overcome the losses associated with any frequency selective feedback network). Hence, to create an oscillator we simply need an amplifier with sufficient gain to overcome the losses of the network that provide positive feedback.
Problem:
1.4 Wien bridge oscillator:
Fig: A Wien bridge network
An alternative approach to providing the phase shift required is the use of a Wien bridge network. Like the C–R ladder, this network provides a phase shift which varies with frequency. The input signal is applied to A and B while the output is taken from C and D. At one particular frequency, the phase shift produced by the network will be exactly zero (i.e. the input and output signals will be in-phase). If we connect the network to an amplifier producing 0° phase shift which has sufficient gain to overcome the losses of the Wien bridge, oscillation will result. The minimum amplifier gain required to sustain oscillation is given by: In most cases, C1 = C2 and R1 = R2, hence the minimum amplifier gain will be 3. The frequency at which the phase shift will be zero is given by: When Rl = R2 and Cl = C2 the frequency at which the phase shift will be zero will be given by: Problem:
1.6: Single-stage astable oscillator
An astable oscillator that produces a square wave output can be built using one operational amplifier, as shown in Fig. The circuit employs positive feedback with the output fed back to the non-inverting inputvia the potential divider formed by R 1 and R 2. When VO = +VCC , capacitor charges towards VUT When VO = - VCC , capacitor charges towards VLT Fig. Single-stage astable oscillator using an operational amplifier When power is turned ON, output VO normally swings either to +Vcc or to - Vcc. Assume : i) C is initially uncharged ii) VO = + V CC The upper threshold voltage (the maximum +ve value at the inverting input) will be given by: The lower threshold voltage (the maximum - ve value at the inverting input) will be given by: Capacitor C charges through R and the voltage VC rise exponentially. As voltage across the capacitor is justgreater than VUT, the output voltage will rapidly fall to − V CC. Capacitor C will then start to discharge through R and the voltage VC, fall exponentially. As voltage across thecapacitor is slightly lesser than VLT, the output voltage will rise rapidly to + V CC.
This cycle will continue indefinitely. Finally, the time for one complete cycle of the output waveform produced by the astable oscillator is given by:
1.7 Crystal controlled oscillators
To obtain a very high level of oscillator stability a Quartz Crystal is generally used as the frequency determining device to produce high frequency stability in oscillators. Such oscillators are called as crystal oscillators. The quartz crystal (a thin slice of quartz in a hermetically sealed enclosure, see Fig.) vibrates whenever a potential difference is applied across its faces (this phenomenon is known as the piezoelectric effect ). The frequency of oscillation is determined by the crystal’s ‘cut’ and physical size. Crystals can be manufactured for operation in fundamental mode over a frequency range extending from 100 kHz to around 20 MHz.
1.9 Operational amplifier parameters
1.Open-loop voltage gain : The open-loop voltage gain of an operational amplifier is defined as the ratio of output voltage to input voltage measured with no feedback applied. Open-loop voltage gain may thus be thought of as the ‘internal’ voltage gain of the device, thus: The open-loop voltage gain is often expressed in decibels ( dB ) rather than as a ratio. 𝑂𝑝𝑒𝑛 𝑙𝑜𝑜𝑝 𝑔𝑎i𝑛 = 20 𝑙𝑜𝑔
𝑉i𝑛 2. Closed-loop voltage gain : The closed-loop voltage gain of an operational amplifier is defined as the ratio of output voltage to input voltage measured with a small proportion of the output fed back to the input. Closed-loop voltage gain is once again the ratio of output voltage to input voltage but with negative feedback is applied, hence:
3. Input resistance : The input resistance of an operational amplifier is defined as the ratio of input voltage to input current expressed in ohms. Input resistance is the ratio of input voltage to input current: where RIN is the input resistance (in ohms), VIN is the input voltage (in volts) and IIN is the input current (in amps) 4. Output resistance : The output resistance of an operational amplifier is defined as the ratio of open-circuit output voltage to short-circuit output current expressed in ohms.
Output resistance is the ratio of open-circuit output voltage to short-circuit output current, hence: where ROUT is the output resistance (in ohms), VOUT(OC) is the open-circuit output voltage (in volts) and IOUT(SC) is the short-circuit output current (in amps).
5. Input offset voltage Practically, a small DC voltage will appear at the output of amplifier when no input voltage (or 0V) is applied. Thus, differential (very small) voltage is required between the inputs to make the output to 0V. Input offset voltage may be minimized by applying relatively large amounts of negative feedback or by using the offset null facility provided by a number of operational amplifier devices. 6. Full-power bandwidth The full-power bandwidth for an operational amplifier is equivalent to the frequency at which the maximum undistorted peak output voltage swing falls to 0.707 of its low frequency (d.c.) value (the sinusoidal input voltage remaining constant). Typical full- power bandwidths range from 10 kHz to over 1 MHz for some high-speed devices. 7. Slew rate : Slew rate is the rate of change of output voltage with time, when a rectangular step input voltage is applied. The slew rate of an operational amplifier is the rate of change of output voltage with time in response to a perfect step function input. Hence:
Vout = - Vin [ 𝐹^ ]
1.10 Operational amplifier characteristics:
Characteristics for an ‘ideal’ operational amplifier are: (a) The open-loop voltage gain should be very high (ideally infinite). (b) The input resistance should be very high (ideally infinite). (c) The output resistance should be very low (ideally zero). (d) Full-power bandwidth should be as wide as possible (ideally infinite). (e) Slew rate should be as large as possible (ideally infinite). (f) Input offset should be as small as possible (ideally zero).
Comparison of operational amplifier parameters for ‘ideal’ and ‘real’ devices
1.11 Operational amplifier configurations
1) Inverting operational Amplifier Input signal Vin is applied to the inverting terminal of the amplifier and output Vout is inverted version(180o^ phase shift) of input Vin. 2) Non-inverting operational Amplifier Input signal Vin is applied to the non-inverting terminal of the amplifier and output Vout is non-invertedversion (0o^ phase shift) of input Vin.
Fig 1 : A voltage follower Fig2: Typical input and output waveforms for a voltage follower Vout = VIN
2. Differentiators A differentiator produces an output voltage that is equivalent to the rate of change of its input. An op-amp differentiator is an inverting amplifier, which uses a capacitor C in series with the input voltage Vin and a feedback resistor R is connected between Vout and inverting (-) input.
3. Integrators: Integrator produces output voltage Vout, is proportional to the integral of the input voltage Vin. An op-amp i ntegrator is an inverting amplifier, which uses a resistor R in series with the input voltage Vin and a capacitor C is connected between Vout and inverting (-) input as feedback.
4. Comparators: A comparator using an operational amplifier is shown in Fig. 8.17. Since no negative feedback has been applied, this circuit uses the maximum gain of the operational amplifier. - The output voltage produced by the operational amplifier will thus rise to the maximum possible value (equal to the positive supply rail voltage)
whenever the voltage present at the non-inverting input exceeds that present at the inverting input.
- Conversely, the output voltage produced by the operational amplifier will fall to the minimum possible value (equal to the negative supply rail voltage) whenever the voltage present at the inverting input exceeds that present at the non-inverting input.
