PHY C21: Inverting & Non-Inverting Amplifiers

Now, let’s take a closer look at negative feedback.

  • Effects of Negative Feedback
  • Inverting amplifiers
    • Virtual earth approximation
  • Non-inverting amplifiers
  • Expressions for voltage gain of inverting & non-inverting amplifiers

Throughout this post, remember the key thing about negative feedback:

The 2 inputs will always try to be at nearly the SAME voltage.

Negative feedback prevents an amplifier from saturating.

This will be handy in understanding its usage below.


What are the benefits of negative feedback?

  • increased bandwidth
  • less output distortion
  • greater stability

What are the applications of negative feedback?
You can create INVERTING & NON-INVERTING AMPLIFIERS.

These differ slightly from the negative feedback shown above since not all of the output voltage is fed back to the inverting input.

Inverting Amplifier
Non-inverting Amplifier

General Characteristics of Amplifiers using Negative Feedback

Resistor connecting the output to the inverting inputAKA feedback resistor
Labelled Rf
Input voltage which can varyLabelled Vin
This is where your input signal would go

Both function in similar ways: I can provide an input signal (maybe from a microphone recording my voice) & the amplifier will amplify it.
The differences between them are where Vin is connected to.

Now, let’s explore each type of amplifier.


Inverting amplifier

How can you identify an inverting amplifier?
Vin is connected to the inverting input.

Before looking at its characteristics, we need to get a concept down first: VIRTUAL EARTH.

What is meant by Virtual Earth?
A point where potential can be approximated to be 0V (Earth).

Why?:

  • an ideal op-amp has infinite gain
  • the non-inverting input is connected directly to the ground, so it is at 0 V
  • remember: negative feedback prevents the amplifier from saturating
  • if the amplifier is not to saturate, the inverting input must be almost at 0 V as well
  • thus, we can say it is at the same potential as the inverting input

What does this mean?
This causes an inverting amplifier to have a gain given by:

Vout/Vin = -Rf/Rin

Here’s why:

Due to negative feedback, the op-amp is unsaturated,
so V+ & V MUST be almost the same.  

Point P is virtual earth, so it is at 0V.
V+ = V = 0
Since Rin is connected between P (0 V) & the input signal (Vin),
the potential difference across Rf MUST be Vin
Vin – 0 = Vin
Since Rf is connected between the output (Vout) & P (0 V),
the potential difference across Rf MUST be –Vout    
0 – Vout = –Vout
No current flows through the inputs.
At the inverting input, all current must flow between the 2 resistors Rin & Rf
 
Since Rin & Rf are in series, the current in them must be EQUAL.Iin = If
Since V = IR, I = V/R
Thus, Iin = Vin/Rin If = –Vout/Rf
Iin = If Vin/Rin = –Vout/Rf  
Rearranging, we get our expression for the gain!Vout/Vin = -Rf/Rin

How does this effect the characteristics of an inverting amplifier?

The gain depends on the ratio of both resistances.

If Rf is a variable resistor, we can manually change the gain (like a volume knob on a speaker!)
Higher Rf means a larger gain (in magnitude, though the sign will be flipped)

Lower Rf means a smaller gain (in magnitude, though the sign will be flipped)
If an alternating input is provided,
there is a phase difference of π rad or 180° between the input & output
When the input is positive, the output will be negative.

When the input is negative, the output will be positive.

On a graph, it looks like this:

Red = input
Blue = output

Non-inverting amplifier

How can you identify a non-inverting amplifier?
Vin is connected to the non-inverting input.

There is no virtual earth point here, unlike an inverting amplifier.

A non-inverting amplifier’s gain is given by:

Vout/Vin = 1 + Rf/R1

Here’s why:

Due to negative feedback, the op-amp is unsaturated,
so V+ & V MUST be almost the same.
V+ = V
Since the non-inverting input is connected to the input signal, V+ is VinV+ = Vin

Thus, V+ = V = Vin
No current flows through the inputs.

At the inverting input, all current must flow between the 2 resistors R1 & Rf
 
Since R1 & Rf are in series, the current in them must be EQUAL.I1 = If
The total potential difference across R1 & Rf is Vout

Now we can consider a potential divider!
V1 + Vf = Vout
Potential difference across R1 can be calculated by considering the potential divider Rf & R1V1 = Vout x R1/(R1 + Rf)
However, we also know that V1 is Vin as R1 is connected between the ground & VV1 = Vin

Thus,
Vin = Vout x R1/(R1 + Rf)
Rearranging to express gain on one side,Vout/Vin = (R1 + Rf)/R1  
Simplifying, we get our expression for the gain!Vout/Vin = 1 + Rf/R1

How does this effect the characteristics of a non-inverting amplifier?

The gain depends on the ratio of both resistances.

If Rf is a variable resistor, we can manually change the gain (like a volume knob on a speaker!)
Higher Rf means a larger gain

Lower Rf means a smaller gain
If an alternating input is provided,
there is no phase difference.
The input & output are IN PHASE.
When the input is positive, the output will be positive.

When the input is negative, the output will be negative.

On a graph, it looks like this:

Red = input
Purple = output

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