Operational Amplifiers and Oscillators PDF

Module 2 Operational amplifiers and Oscillators  Operational amplifiers : Introduction An operational amplifier (or OP AMP) is a very high gain differential amplifier with high input impedance and low output impedance. Op amp offer all the advantages of monolithic inte...

Module 2 Operational amplifiers and Oscillators  Operational amplifiers : Introduction An operational amplifier (or OP AMP) is a very high gain differential amplifier with high input impedance and low output impedance. Op amp offer all the advantages of monolithic integrated circuit such as small size, high reliability, reduced cost and less power consumption. Op amps are used in used in applications such as adder, subtractor, multiplier, integrator, differentiator, rectifier, comparator, instrumentation amplifiers etc. Figure 8.1 A typical operational amplifier. Internal Circuit of IC741  Symbols and Connections The device has two inputs i.e. inverting input & non-inverting input and one output and no common connection. Inverting input is marked by “−” sign & Non-inverting input is marked by “+” sign. The ‘+’ sign indicates zero phase shift while the ‘−’ sign indicates 180° phase shift. Opamp requires symmetrical supplies i.e. positive and negative rail supply (±6 V to ±15 V) to allow the output voltage to swing both positive (above 0 V) and negative (below 0 V).  Operational Amplifier Parameters The various operational amplifier parameters are as follows: a) Open loop gain b) Closed loop gain c) Input Resistance d) Output Resistance e) Input offset voltage f) Full Power Bandwidth g) Slew Rate  Operational Amplifier Parameters a) Open-loop voltage gain It is ratio of output voltage to input voltage measured with no feedback applied. Open loop gain (Av(OL)) is the internal voltage gain of opamp and is given by expression In decibels, where Vin & Vout is the input & output voltage respectively under open loop conditions. Most operational amplifiers have very high open-loop voltage gains values (Typically Av(OL) > 100000 or Av(OL) > 90 dB).  Operational Amplifier Parameters b) Closed-loop voltage gain It is ratio of output voltage to input voltage measured with negative feedback applied. Open loop gain (Av(CL)) is the internal voltage gain of opamp and is given by expression In decibels, where Vin & Vout is the input & output voltage respectively under closed loop conditions. Closed-loop voltage gain is normally very much less than the open-loop voltage gain.  Operational Amplifier Parameters c) Input Resistance It is defined as ratio of input voltage to input current and is given by expression: where Rin is the input resistance (in ohms), Vin is the input voltage (in volts) and Iin is the input current (in amps). The input of an operational amplifier is purely resistive at lower frequencies. However, at high frequencies the shunt capacitive reactance become more significant. Input resistance of operational amplifiers is very much dependent on the semiconductor technology employed. In practice values range from about 2 MΩ for common bipolar types to over 1012 Ω for FET and CMOS devices.  Operational Amplifier Parameters d) Output Resistance It is defined as ratio of open-circuit output voltage to short-circuit output current and is given by expression: where, Rout is the output resistance (in ohms), Vout(OC) is the open-circuit output voltage (in volts) and Iout is the short-circuit output current (in amps). Typical values of output resistance range from less than 10 Ω to around 100 Ω, depending upon the configuration and amount of feedback employed.  Operational Amplifier Parameters e) Input offset voltage An ideal operational amplifier would provide zero output voltage when 0 V difference is applied to its inputs. In practice, due to imperfect internal balance, there may be some small voltage present at the output. The voltage that must be applied differentially to the operational amplifier input in order to make the output voltage exactly zero is known as the input offset voltage. 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. Typical values of input offset voltage range from 1mV to 15mV. If AC rather than DC coupling is employed, offset voltage is not normally a problem and can be happily ignored.  Operational Amplifier Parameters f) Slew Rate It is the maximum rate of change of output voltage with time in response to a perfect step-function input and is given by expression: where ∆VOUT is the change in output voltage (in volts) and ∆t is the corresponding interval of time (in seconds). Slew rate is measured in V/s (or V/μs) and typical values range from 0.2 V/μs to over 20 V/μs. Slew rate imposes a limitation on circuits in which large amplitude pulses rather than small amplitude sinusoidal signals are likely to be encountered.  Operational Amplifier Parameters g) Full Power Bandwidth It is defined as the maximum frequency at which the op-amp will yield an undistorted ac output with the largest possible signal amplitude. Typical full-power bandwidths range from 10 kHz to over 1 MHz for some high-speed devices. Example 8.1 An operational amplifier operating with negative feedback produces an output voltage of 2V when supplied with an input of 400μV. Determine the value of closed-loop voltage gain. Example 8.2 An operational amplifier has an input resistance of 2 MΩ. Determine the input current when an input voltage of 5 mV is present. Example 8.3 A perfect rectangular pulse is applied to the input of an operational amplifier. If it takes 4 μs for the output voltage to change from –5 V to +5 V, Determine the slew rate of the device. Example 8.4 A wideband operational amplifier has a slew rate of 15 V/μs. If the amplifier is used in a circuit with a voltage gain of 20 and a perfect step input of 100 mV is applied to its input, determine the time taken for the output to change level.  Operational Amplifier Characteristics The desirable characteristics for an ‘ideal’ operational amplifier are: a) Open-loop voltage gain should be very high (ideally infinite). b) Input resistance should be very high (ideally infinite). c) Output resistance should be very low (ideally zero). d) Full-power bandwidth should be as wide as possible. e) Slew rate should be as large as possible. f) Input offset should be as small as possible. The characteristics of most modern integrated circuit operational amplifiers (i.e. ‘real’ operational amplifiers) come very close to those of an ‘ideal operational amplifier, as witnessed by the data shown in Table 8.1.  Operational Amplifier Circuits Inverting Amplifier An inverting amplifier is one whose output is amplified and is out of phase by 1800 with respect to the input. The gain expression is given by: The negative sign in the equation indicates an inversion of the output signal with respect to the input as it is 180o out of phase. This is due to the feedback being negative in value. The equation for the output voltage Vo also shows that the circuit is linear in nature for a fixed amplifier gain as Vo = Vin x Gain. This property can be very useful for converting a smaller sensor signal to a much larger voltage.  Extra There are two very important rules to remember about Inverting Amplifiers or any operational amplifier for that matter and these are. No Current Flows into the Input Terminals. The Differential Input Voltage is Zero as V1 = V2 = 0 (Virtual Earth) By KCL we have  Operational Amplifier Circuits Non-inverting Amplifier A non-inverting amplifier is an operational amplifier circuit with an output voltage that is in phase with the input voltage. The gain expression is given by: The gain will never be less than 1, so the non-inverting op amp will produce an amplified signal that is in phase with the input.  Operational Amplifier Circuits Voltage follower Voltage follower is one whose output is equal to the input. The voltage follower configuration shown here is obtained by short circuiting “Rf” and open circuiting “R1” connected in the usual non-inverting amplifier. Thus all the output is fed back to the inverting input of the op-amp. The output expression is given by: Therefore the output voltage will be equal and in-phase with the input voltage. The result is an amplifier that has a voltage gain of 1 (i.e. unity), a very high input resistance and a very high output resistance. This stage is often referred to as a buffer and is used for matching a high-impedance circuit to a low-impedance circuit.  Problems An Op-Amp non-inverting amplifier has an input resistance of 10KΩ and Feedback resistance of 50KΩ. If the input voltage is 0.5V, find the output voltage. For the following Op-amp circuit, Rin = 1000Ω and gain A = -75. Determine the value of feedback resistance.(VCC = 12V and –VEE = -12V). For the following Op-amp circuit, Rg = 12KΩ and gain A = 50. Determine the value of feedback resistance. (VCC = 12V and –VEE = -12V).  Problems Determine the output voltage for the circuit shown in figure with a sinusoidal input of 2.5 mV. Design an inverting amplifier to have a gain of -10 and an input resistance of 10Kohm.  Operational Amplifier Circuits Operational amplifiers have a number of other applications such as : a) Summer (Summing Amplifier) b) Subtractor (Difference Amplifier) c) Integrator d) Differentiator  Operational Amplifier Circuits Summing amplifiers A summing amplifier is a circuit that produces an output that is the sum of its two input voltages. Since the operational amplifier is connected in inverting mode, the output voltage is given by: where V1 and V2 are the input voltages. A typical application is that of ‘mixing’ two input signals to produce an output voltage that is the sum of the two.  Operational Amplifier Circuits Summing amplifiers (with different input resistances)  Operational Amplifier Circuits Difference/differential amplifiers (subtractor) – The differential amplifier amplifies the voltage difference present on its inverting and non-inverting inputs. – By connecting one voltage signal onto one input terminal and another voltage signal onto the other input terminal the resultant output voltage will be proportional to the “Difference” between the two input voltage signals of V1 and V2. – If all the resistors are equal, that is: RF = RIN, then the circuit will become a Unity Gain Differential Amplifier and the voltage gain of the amplifier will be exactly one or unity. Then the output expression would simply be Vout = V2 – V1.  Operational Amplifier Circuits Differentiator A differentiator produces an output voltage that is equivalent to the rate of change of its input. The expression is given by: Integrator An integrator produces an output which is equivalent to the area under the graph of the input function. The expression is given by:  Problems The summing amplifier as shown in below figure has Rf = 10KΩ, R1 = 10KΩ, R2 = 2.2KΩ and R3 = 3.3KΩ, If V1 = 6V, V2 = -3V, V3 = -0.75V, Find Vout Calculate the output voltage of the circuit shown in figure, if V1= - 0.2V and V2=0V. Draw the output waveform of an Op-Amp – If square wave is given at the differentiator input. – If triangular wave is given at the differentiator input  Problems Identify the circuit shown in figure. When a sine wave of 1vpeak at 1000Hz is applied to the circuit with the following specification: RF =1kΩ and C1=0.33µF, find its output waveform and its output equation. Design an appropriate circuit using Op-amp, whose input and output signals relations are as shown in figure. Also justify your answer with relevant equations.  Positive feedback (Extra) Positive feedback is an alternative form of feedback, where the output is fed back in such a way as to reinforce the input (rather than to subtract from it). The overall voltage gain (G) of amplifier with positive feedback is given by: where Av is the internal gain of the amplifier & β is the proportion of the output voltage fed back to the input. when the loop gain, βAv, approaches unity. The denominator (1 − βAv) will become close to zero. Therefore, the overall gain with positive feedback applied will be greater than the gain without feedback. This form of feedback is used in oscillator circuits.  Oscillators Oscillators are the circuits that generate an output signal without the need for an input signal. When the loop gain approaches unity (or larger), it results in unstable amplifier with infinite gain. In such case, amplifier will oscillate since any disturbance will be amplified and result in an output. Therefore, positive feedback have an undesirable effect i.e. instead of reducing the overall gain it reinforces any signal present and the output continuous oscillates if the loop gain is 1 or greater.  Condition for Oscillations There are two conditions for oscillation a) the feedback must be positive (i.e. the signal fed back must arrive back in-phase with the signal at the input); 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). To create an oscillator, an amplifier with sufficient gain is needed to overcome the losses of the network that provide positive feedback. If the amplifier provides 180° phase shift, the frequency of oscillation will be that at which there is 180° phase shift in the feedback network. Alternatively, if the amplifier produces 0° phase shift, the circuit will oscillate at the frequency at which the feedback network produces 0° phase shift. Positive feedback is needed in both cases so that the output signal arrives back at the input in such a sense as to reinforce the original signal.  Classification of Oscillators Electronic oscillators are classified mainly into the following two categories − Sinusoidal Oscillators − The oscillators that produce an output having a sine waveform are called sinusoidal or harmonic oscillators. Such oscillators can provide output at frequencies ranging from 20 Hz to 1 GHz. Non-sinusoidal Oscillators − The oscillators that produce an output having a square, rectangular or saw-tooth waveform are called non-sinusoidal or relaxation oscillators. Such oscillators can provide output at frequencies ranging from 0 Hz to 20 MHz.  Ladder Network Oscillator A phase shift oscillator based on 3-stage C–R ladder network can be used to provide 180° phase shift. The total phase shift provided by the C–R ladder network (connected between collector and base) is 180° at the frequency of oscillation. The op-amp in inverting amplifier configuration provides the other 180° phase shift in order to realize an overall phase shift of 360° or 0° (note that these are the same). The frequency of oscillation is The loss associated with the ladder network is 29, thus the amplifier must provide a gain of at least 29 in order for the circuit to oscillate. They can be used in applications such as musical instruments, GPS units, voice synthesis etc.  Wien Bridge Oscillator A phase shift oscillator based on a Wien bridge network can be used to provide 0° phase shift. Similar to 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 (called resonant frequency), the phase shift produced by the network will be exactly zero and feedback component is maximum. If an amplifier producing 0° phase shift is connected which has sufficient gain to overcome the losses of the Wien bridge, oscillations will result. The frequency at which the phase shift will be zero is : The minimum amplifier gain required to sustain oscillation is : They can be used in audio applications, capacitance measurement, etc. Example 9.1 Determine the frequency of oscillation of a three stage ladder network oscillator in which C = 10 nF and R = 10 kΩ. Example 9.2 Fig. 9.4 shows the circuit of a Wien bridge oscillator based on an operational amplifier. If C1 = C2 = 100 nF, determine the output frequencies produced by this arrangement (a) when R1 = R2 = 1 kΩ and (b) when R1 = R2 = 6 kΩ. Assignment Problems 1. Estimate the values of R and C for an output frequency of 2kHz in a RC ladder network oscillator. 2. In a ladder network oscillator that uses three RC sections, R = 10 kΩ. If the oscillator is to generate frequencies in the range from 1KHz to 100 kHz, what should be the range of C?  Crystal Controlled Oscillators Crystal controlled oscillators are used when an exact frequency of oscillation need to be accurately maintained. Crystal oscillator used quartz crystal as the frequency determining element and operates on the principle of piezoelectric effect. During piezoelectric effect, whenever a potential difference is applied across its faces of quartz crystal, the crystal oscillates. The frequency of oscillation is determined by the crystal’s ‘cut’ and physical size. If an AC voltage is applied, the crystal starts vibrating at the frequency of the applied voltage. However, if the frequency of the applied voltage is made equal to the natural frequency of the crystal, resonance takes place and crystal vibrations reach a maximum value.  Crystal Controlled Oscillators The figures below represent the symbol and electrical equivalent circuit of a crystal respectively. The equivalent circuit consists of a series R-L-C circuit in parallel with a mounting capacitance Cm. The first one is the series resonant frequency (fs), which occurs when reactance of the inductance (L) is equal to the reactance of the capacitance C. The second one is the parallel resonant frequency (fp), which occurs when the reactance of R-L-C branch is equal to the reactance of capacitor Cm. Where, Problems The parameters of a crystal fitted in a crystal oscillator are as follows: L = 0.4H, C = 0.08pF, CM = 1pF and R = 6kΩ. Determine (i) The series resonant frequency (ii) The parallel resonant frequency