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
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 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
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
