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Operational Amplifier (Op-amp)

  • The output is proportional to the difference between the two input voltages, given by:
    • Vout = A0(V+ – V)
    • where V+ and V are the voltages at the non-inverting and inverting terminals and A0 is the open-loop gain
  • When the calculated output of an op-amp is greater than the supply voltage, the op-amp is said to be saturated and the output is equal to the supply voltage
  • If the output is not saturated, the two inputs are virtually at the same voltage
  • If V+ > V, then the output is positive
  • If V+ < V, then the output is negative
Ideal Operational Amplifier Properties
  • Infinite Input Impedance: No current enters or leaves either of the inputs
  • Zero Output Impedance: The whole of the voltage voltage is provided across the output load
  • Infinite Open-loop Gain: Even if there is only a slight difference between the input voltages, the op-amp will be saturated and the output will equal the supply voltage
  • Infinite Bandwidth: All frequencies are amplified by the same factor
  • Infinite Slew Rate: There is no delay between changes in the input and consequent changes in the output
  • Zero Noise Contribution: An ideal op-amp does not produce any noise itself
  • An op-amp can be used to compare the two inputs and the output will switch from one saturation level to the other when one of the input voltages changes
  • The inverting and non-inverting inputs are derived from two potential dividers, so only very small current flow.
  • This examples shows a comparator being used to operate a small lamp when it gets dark
  • In daylight, the LDR has low resistance (3 kΩ) and the non-inverting voltage is small, causing the op-amp to be negatively saturated (-9 V).
    • Diode reverse-biased: lamp doesn’t light
    • At A: 3/12 + 3 × 9 = 1.8 V
    • At B: 15/15 + 15 × 9 = 4.5 V
    • 1.8 – 4.5 = 2.7, therefore -ve saturation
  • In darkness, the LDR has high resistance (18 kΩ) and the non-inverting voltage is high, causing the op-amp to be positively saturated
    • Diode forward-biased: lamp lights
    • At A: 18/12 + 18 × 9 = 5.4 V
    • At B: 15/15 + 15 × 9 = 4.5 V
    • 5.4 – 4.5 = 0.9, therefore +ve saturation
  • The LDR could be replaced by other sensors.
Negative Feedback
  • A fraction βof the output is fed back to the inverting input of the op-amp
  • Though the negative feedback reduces the voltage gain of the amplifier, it will improve the accuracy and control
  • Advantages of Negative Feedback:
    • It increases the range of frequencies over which the voltage gain is constant (increased bandwidth)
    • The amplifier is more stable
    • There is less distortion
Inverting Amplifier
  • The input voltage is applied to the inverting input through the input resistance R
  • The non-inverting input is connected to zero-volt
  • Negative feedback is applied to the inverting input through a resistor Rf
  • The non-inverting input is at virtual earth:
    • the op-amp hav a very large gain
    • and the non-inverting input is earthed
    • If the amplifier is not to saturate, inverting input must be (almost) at the earth potentials
  • Since the input resistance of the op-amp is infinite, current in Rin = current in Rf
  • Hence: p.d. across Rin/Rin = p.d. across Rf/Rf
  • The potential at P is zero (virtual earth), so Vin – 0/Rin = 0 – Vout/Rf
  • Therefore, the overall voltage gain is given by
    • Voltage gain = Vout/Vin = Rf/Rin
Non-inverting Amplifier
  • The input voltage is applied to the non-inverting input
  • Negative feedback is provided by a potential divider consisting of resistors R1 and Rf
  • As before, the current in the two resistors are equal and can written as
    • Vout/(Rf + R1) = Vin/R1
  • Cross multiply and rearrange
    • Vout/Vin = Rf + R1/R1
  • Therefore, the overall voltage gain is given by;
    • Voltage gain = Vout/Vin = 1 + Rf/R1
  • The output of op-amp cannot exceed 25 mA and 15 V so in order to operate electronic circuits which require large currents, a relay must be used at output of the op-amp
  • A relay is an electromagnetic switch that can switch on or off a large current using a small current
  • It consists of an electromagnet, which when energized by the small current, operates the contact, switching on or off the large current
  • The diode D2 conducts only when the output of the op-amp is positive with respect to the earth
  • A back e.m.f. is generated by the coil when the current in the relay is switched off, which may damage the op-amp
  • The diode D1, connected across the coil, protects the op-amp from back e.m.f. by conducting this current
Light Emitting Diode (LED)
  • A LED is a diode which emits light only when it is forward-biased, hence it can be used to indicate the state of the output of an op-amp
  • The maximum allowed current through a forward-biased LED is 20 mA and has a breakdown voltage of about 5 V
  • Hence, to protect a LED from large currents, a resistor is connected in series with it
  • When the output is positive, the diode D1 is forward-biased and will conduct, emitting light
  • When the output is negative, the diode D2 is reverse-biased and will conduct, emitting light
Calibration Curve
  • To measure the output voltage of an op-amp, an analogue or digital voltmeter is required
  • Using a calibration curve, we can match this output voltage to a physical quantity
  • For example, to set the temperature for frost warning, a calibration curve between the temperature of the thermistor and the corresponding output voltage is created
    • The output voltage corresponding to the frost warning temperature can be obtained from the calibration curve
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