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### Op Amps

Operation Amplifiers (op-amp)
The ideal op-amp has open-loop, gain infinite, infinite bandwidth, Infinite input impedances so that no current is drawn, Zero output impedance so that maximum current is transferred to the load, input offset zero and no thermal drift.

The ratio of the input to the output voltage with no feedback resistor is called the open-loop voltage gain. It’s the gain of the amplifier or the gain at a frequency of 1 Hz. But the opposite of this is of course the voltage gain with a feedback resistor called closed loop voltage

The maximum frequency in which the gain response of the system is maintained is called the Bandwidth.

With the op-amp circuit having a voltage gain of unity the slew rate is the time rate of change of the output voltage. This represents the fastest response that an op-amp can have.
Slew rate limits the large-signal response of the op-amp. This finite time response is due to the presence of a compensating capacitor within the op-amp internal circuitry.
The formula for slew rate of an op-amp is : SR = Vout/t

Formula for inverting op amp
Use Kirchhoff’s current rule I1 + I2 = 0
Vin/Rin = -Vout / Rf
Vout/Vin = - Rf / Rin
So Gain = - Rf / Rin

Non Inverting op amps formula
Vin = Vout (Rin / Rf + Rin)
Vin / Vout = Rin / Rf + Rin
Invert both sides Vout / Vin = Rf + Rin / Rin
Vout / Vin = 1 + Rf / Rin

Example: 1) Feedback resistance (Rf) = 5000 and input resistance (Rin) = 2000
Vout/Vin = 5/2 +1
Voltage Gain = 3.5
2) If Rf = Rin then
Gain = 1 +1 = 2
3) In a non inverting op-amp circuit, what is the voltage gain if: Rf = 82k and
Rin = 6.8k
Gain is Vout/Vin so use Vout/Vin = 1Rf/Rin
Vout/Vin = 1+ 82K/6.8K
So Gain = 13.06
4) Choose a Feedback resistor for a no inverting op-amp if Rin =1K, Vin =100mV and output = 10V
Use Vout / Vin = 1 + Rf/Rin
Rearrange Rin * Vout/ Vin - 1 = Rf
So Rf= 1K x 10V/0.1V - 1

5) Find the voltage Gain for a non inverting op-amp with Rf 12K and Rin = 2K
Use Vout/ Vin = 1 + Rf/Rin
So Vout/Vin = 12k/2k
= 6 +1
= 7
A Voltage Follower is used as a Buffer Amplifier and has;the input connected into the non-inverting input, no feedback or input resistors, a gain of 1 or unity just like a 1 to 1 BJT. It is used to match high impedance input source with a low impedance load for example a speedometer signal that needs to be sent to the ECU with changing the reading but the speedo transducer output doesn’t have the current to sent it so a voltage follower is used to send the signal to more than 1 device without changing it.

Summing Amplifier

The summing amplifier is a handy circuit enabling you to add several signals together. These are used in digital to analogue conversion. An audio mixer is a good example of adding waveforms from different channels (vocals, instruments) together before sending the combined signal to a recorder or speaker. They have a virtual earth at the inverting input. The output is the sum of all the input signals but is of opposite polarity.
-       Vout /Rf = V1/R1 + V2/R2 + V3/R3
-       Vout = -Rf ( V1/R1 + V2/R2 + V3/R3)

Example 1)
An op-amp has 2 inputs, one having a resistance of 3K and the other an input resistance of 8K. The two inputs have a voltage of + 8 V and + 12 V respectively. The feedback resistance is 5K. What’s the output voltage?
-       Because we want the output voltage use the formula Vout = -Rf ( V1/R1 + V2/R2)
This gives: Vout = -5000 x (8/3000 + 12/5000)
= -25.3V which means inverted 25.3V
2)
An op-amp has 3 inputs, one having a resistance of 1000 with 5V supply, the
second 5000 with 10V supply and the third 10K with 4 volts supply respectively.
The feedback resistance is 2000. What is the output voltage?
Vout = -Rf(V1/R1 + v2/R2+ V3/R3)
Vout = -2000(5/1000 + 10/5000 + 4/10000)
Vout = -14.8V
=inverted 14.8V

Comparator Op-amp
The operational amplifier (op-amp) has a well balanced difference input and a very high gain. The parallels in the characteristics allow the op-amps to serve as comparators in some functions.
A standard op-amp operating in open loop configuration (without negative feedback) can be used as a comparator. When the non-inverting input (V+) is at a higher voltage than the inverting input (V-), the high gain of the op-amp causes it to output the most positive voltage it can. When the non-inverting input (V+) drops below the inverting input (V-), the op-amp outputs the most negative voltage it can. Since the output voltage is limited by the supply voltage, for an op-amp that uses a balanced, split supply, (powered by ± VS) this action can be written: Vout = Ao(V1-V2)
They have a slew rate due to an internal compensation capacitor at the slowest they can be tens of microseconds, designed to operate in the linear mode with negative feedback

Differential Op-amp

Differential Op-amps use the longest and most complex formula of all the previously motioned op-amps. It makes use of both, non-inverting and inverting inputs with a gain to give an output the same as the difference of the two inputs. If R1=R2=R3=R4 then gain=1. But the upper and lower resistors can be changed to alter the gain to a value higher or lower than one. If we are to use resistors of different values we have to find the non-inverting and inverting voltage inputs.
The Voltage divider rule: V+ = V1 (R2/R1+R2) is used to find V+
The Non-inverting gain equation: Vout1 = V+(G+) = V1(R2/R1+R2)(R3+R4/R3) is used to find the non-inverting Vout. The inverting gain equation is used to calculate the stage gain for VOUT2. These inverting and non-inverting gains are then added in.
When R2 = R4 and R1 = R3, the equation can be simplified.
It is now obvious that the differential signal, (V1–V2), is multiplied by the stage gain, so the name differential amplifier suits the circuit. Because it only amplifies the differential portion of the input signal, it rejects the common-mode portion of the input signal.