Operational Amplifier (Op-amp)

• The output is proportional to the difference between the two input voltages, given by:
  • V_out = 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

Comparator

• 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 R_f
• 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 R_in = current in R_f
• Hence: ^{p.d. across R_in}/_Rin = ^{p.d. across R_f}/_Rf
• The potential at P is zero (virtual earth), so ^{V_in – 0}/_Rin = ^{0 – V_out}/_Rf
• Therefore, the overall voltage gain is given by
  • Voltage gain = ^V_out/_Vin = ^R_f/_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 R_f
  
• As before, the current in the two resistors are equal and can written as
  • ^V_out/_{(Rf + R1)} = ^V_in/_R1
• Cross multiply and rearrange
  • ^V_out/_Vin = ^{R_f + R₁}/_R1
• Therefore, the overall voltage gain is given by;
  • Voltage gain = ^V_out/_Vin = ^{1 + R_f}/_R1

Relays

• 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