## Non-Inverting Amplifier

### Introduction

An amplifier is an analogue circuit. This page is about a voltage amplifier based on an Op-Amp. The output voltage (Vout) of the circuit depends on the input voltage (Vin) and the Gain (Av) of the circuit.

It is a good idea to read the amplifier basics page first.

For all the circuits shown below, the amplifier is assumed to a have a positive and a negative power supply, usually ±15V, so that the output voltage can be both positive and negative.

### Basic Non-Inverting Amplifier Circuit

The Op-Amp needs to have ± power supplies (assumed to be ±15V)

The input, Vin, is connected directly to the non-inverting input

The circuit uses a feedback resistor (Rf) and an input resistor (Ri) to feedback a fraction of the output voltage to the inverting input. Ri and Rf form a potential divider

Ri is not the actual input resistor but the same naming convention is used to be consistent with the inverting amplifier

Voltage gain (Av) is determined by Ri and Rf

The voltage gain is given by:

Av = 1 + Rf / Ri

Note: Ri and Rf should both be >1kΩ and <10MΩ

Note: The voltage gain of the Non-Inverting amplifier cannot be less than unity (1) and so this amplifier cannot be used to attenuate signals

### Function of the Non-Inverting Amplifier

The output voltage is directly proportional to the input voltage (as long as the output is not saturated) such that:

Vout = Av × Vin

If the input voltage is positive, the output voltage is also positive
If the input voltage is negative, the output voltage is also negative

The graph shows the transfer characteristics (Input Voltage and Output Voltage) for a Non-Inverting amplifier with a voltage Gain of +2

When Vin = +5V then Vout = +10V and when Vin = −5V then Vout = −10V

The Output Voltage is limited to ±13V by the power supply of the amplifier. Therefore, when Vin > +6.5V then Vout saturates at +13V and when Vin < −6.5V then Vout saturates at −13V (shown by the horizontal lines on the graph)

The graph shows the relationship between the Input Voltage and Output Voltage of a Non-Inverting amplifier with a voltage Gain of +2 when the input is an A.C. voltage

At all times Vout = +2 × Vin

### Example Circuits

The voltage gain is:

Av = 1 + (220 ×103 / 100 ×103) = +3.2

If Vin = +1.0V then Vout = +3.2V

The Input Voltage has been amplified (made bigger)

The voltage gain is:

Av = 1 + (47 ×103 / 100 ×103) = +1.47

If Vin = +1.0V then Vout = +1.47V

The Input Voltage has been amplified even though Rf is smaller than Ri

The voltage gain is:

Av = 1 + (100 ×103 / 100 ×103) = +2.0

If Vin = +1.0V then Vout = +2.0V

The Input Voltage has been amplified by a factor of two

The voltage gain is:

Av = 1 + 0 / 100 x103 = +1.0

This is a unit gain amplifier - the Output Voltage has the same amplitude as the Input Voltage. This amplifier is a buffer as the input takes almost no current from the voltage source but provides a reasonable current to the subsequent circuits

### Gain and Bandwidth

The two main parameters of the Inverting Amplifier are the gain and the bandwidth. Increasing the gain reduces the bandwidth and vice versa.

For a Non-Inverting amplifier based on a standard Op-Amp the relationship between gain and bandwidth is approximately:

gain × bandwidth = 106

The graph shows that as gain increases, bandwidth decreases. Note that both scales are logarithmic

When the gain is ×1 (blue line) the amplifier works effectively up to frequencies of 1MHz. If the gain is increased to ×10 (green line)the amplifier only works effectively up to about 100kHz (still okay for audio) but at a gain of ×1000 (red line)the amplifier only works effectively up to a frequency of 1KHz before the gains starts to reduce and the Output Voltage starts to decrease

If the gain is +100, the bandwidth is 10kHz

If a bandwidth of 40kHz is required, the maximum gain is +25

### Better Non-Inverting Amplifier Circuit

When used in reality, amplifiers are often decoupled which means that the input and output are connected through capacitors to stop any spurious D.C. signals compromising the performance of the amplifier. Depending on what the amplifier is attached to, a resistor may also be needed on the output down to 0V.The input resistance of the Op-Amp is very high meaning that small currents can become relatively large voltages (V=IR) at the input increasing the random noise of the amplifier. To avoid this, an input resistor is often connected to ground to lower the effective input resistance of the amplifier.

The capacitor on the input is usually a non-electrolytic type, nominally 1µF or less. The capacitor on the output is ideally a non-electrolytic type but sometimes larger value electrolytic capacitors need to used if the amplifier is providing significant current to the next stage

The addition of capacitors and resistors to the input and output can reduce the bandwidth of the amplifier

### How the Non-Inverting Amplifier works (Advanced)

When considering amplifiers made from Op-Amps there are two basic assumptions:

• The open loop gain (A0) of the Op-Amp is very large
• No current flows in to the inverting and non-inverting inputs

Negative Feedback

• Recall that Vout = A0 × (V+ − V) where A0 = 106 and so a difference between V+ and V of more than a few µV will result in a large (saturated) output voltage
• The feedback resistor ensures that voltage at the inverting input is very similar (within a few microvolts) to the voltage at the non-inverting input
• As the non-inverting input is connected directly to the Input Voltage (Vin) then the inverting input must also be very close to the Input Voltage - within a few µV or so
• Rf and Ri form a potential divider with Vout at one end, 0V at the other end and the inverting input at approximately Vin in the middle
• The feedback works because if Vin is positive and rises, the voltage at the output rises very rapidly as a consequence because there is a difference between the inverting and non-inverting inputs which causes Vout to change. As the non-inverting input is bigger than the inverting input in this case then Vout becomes more positive. As Vout becomes more positive the voltage at the inverting input also rises until it is approximately Vin once more. Therefore a change in the Input Voltage causes a corresponding change in the Output Voltage to keep the inverting input at (or very close to) the non-inverting input

Gain Equation

• Assume Vin is positive (as shown in the diagram above)
• The feedback current in the input resistor is given by I = Vin / Ri because the voltage at the inverting input is Vin due to the negative feedback and so this is the potential difference across the resistor
• As no current flows in to the inverting input, the current in the input resistor also flows through the feedback resistor
• To make current flow through the feedback resistor as shown, Vout must be greater than Vin
• The potential difference across the feedback resistor is therefore Vout − Vin
• Therefore, I = (Vout − Vin) / Rf
• Equating the currents leads to the gain equation
• Recall, gain is defined as: Gain = Vout / Vin

We have

I = Vin / Ri = (Vout − Vin) / Rf

and therefore

Gain = Vout / Vin = 1 + (Rf / Ri)