# 6 - Operational Amplifiers

##### 2016-05-18 11:39:00 +0000, 2 years and 4 months ago

An Op amp is a voltage amplifier which amplifies the differences between two input voltages to decide if the output should be high or low depending on these inputs. Op amps usually require a dual rail, DC supply.

The symbol of an Op amp is shown below:

Where V+ = non-inverting input \ V- = inverting input
+Vs = positive supply rail
-V- = negative supply rail \

Vout is found by using the following calculation:

Where A = open loop gain (10^6)
A theoretical op-amp is assumed to have the following behaviours:

• Very large open loop gain (10^6)
• Vout = Vs (in reality it is +Vs - 2V and Vs + 2V)
• Infinite input impedance, so no current passes
• Zero output impedance, so any current can be outputted
• Vout = 0V when; V+ = V-

6.01 - gain bandwidth product

Most op-amps have high voltage gains, up to 10^6, such large voltage gains require care, so not to oscillate the input. The output terminals must be well separated from the input terminals to prevent positive feedback from stray capacitance.

To ensure the op-amp is stable, a small capacitor is added between the output and the inverting input terminal. This helps to reduce the voltage gain with increasing input frequency.

The graph below shows the directly proportional linear relationship between frequency and voltage gain of the op-amp.

10^6|\
| \
|   \
10^5|     \       y = Open loop voltage gain / Volts
|       \     x = frequency / Hertz
|         \
10^4|           \
|             \
|               \
10^3|                 \
|                   \
|                     \
10^2|                       \
|                         \
|                           \
10^1|                             \
|                               \
|                                 \
10^0+------------------------------------
10^0   10^2   10^3   10^4  10^5  10^6
`

As shown from the graph, voltage gain decreases as frequency input increases , at 10^6Hz, the voltage gain has fallen to 1; no voltage gain. This is summarised in the following equation:

In order to create circuits with high bandwidths and high voltage gains it is necessary to use several low-gain op-amp circuits cascaded together.

6.02 - feedback

Feedback occurs when part of the output is allowed back into the input, this can occur in two ways; to cancel out part of the input signal, Negative Feedback, or it can reinforce the input signal, Positive Feedback.

Negative Feedback:
This is when part of the output signal is fed-back into the input with a phase-shift of 180 degrees (wave is flipped, positive is negative, vice versa). This has the effect of cancelling out part of the input signal, thus reducing the overall voltage gain.
Negative feedback is used to reduce voltage gain to set amount, thus increasing the bandwidth of the circuit and reducing any distortion that may been introduced by the amplifier.

Positive Feedback:
This is when a proportion of the output is fed-back into the input with a phase-shift of 0 degrees. This has the effect of increasing the input signal and thus increasing the overall gain of the circuit. All oscillators and astable circuits rely on positive feedback to make them unstable, and thus oscillate.
It is important that the output circuit is kept as far away as possible from the input circuit. Failure to do so will result in the amplifier system to be unstable, oscillate very strongly and almost uncontrollable.
Any unexplainable increase in voltage gain of an amplifier is a good indicator that the system is not as stable as it should be.

6.03 - amplifier subsystems

An amplifier is designed to produce and output voltage or current that is an enlarged copy of the input voltage or current. When power amplification occurs, extra power is provided by an external power supply. The peak power output is limited by the power supply voltage. The gain is calculated via the ratio of the output voltage, to the input voltage.

6.05 - negative feedback

Since the open-loop voltage gain of an op-amp is too large to be of practical use as an amplifier, and since it is not possible to adjust the open-loop voltage gain, it is necessary to reduce the overall gain of the circuit using negative feedback to cancel out part of the input signal. With negative feedback part of the output signal is fed back into the input with a phase shift of 180 degrees (flips the signal, positive is negative, vice versa). Cancelling out part of the input signal has the effect of reducing the overall gain of the input signal; whilst the actual open-loop gain is unchanged itself.

6.06 - positive feedback

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