*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 input | AKA feedback resistor Labelled R _{f} |

Input voltage which can vary | Labelled V_{in}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 V _{in} is connected to.**

*Now, let’s explore each type of amplifier.*

__Inverting amplifier__

__Inverting amplifier__

__How can you identify an inverting amplifier?__

V_{in} 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:

## V_{out}/V_{in} = -R_{f}/R_{in}

**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 R_{in} is connected between P (0 V) & the input signal (V_{in}),the potential difference across R _{f} MUST be V_{in} | V_{in} – 0 = V_{in} |

Since R_{f} is connected between the output (V_{out}) & P (0 V),the potential difference across R _{f} MUST be –V_{out} _{ } | 0 – V_{out} = –V_{out} |

No current flows through the inputs. At the inverting input, all current must flow between the 2 resistors R _{in} & R_{f} | |

Since R_{in} & R_{f} are in series, the current in them must be EQUAL. | I_{in} = I_{f} |

Since V = IR, I = V/R Thus, I _{in} = V_{in}/R_{in} I_{f} = –V_{out}/R_{f} | I_{in} = I_{f} V_{in}/R_{in} = –V_{out}/R_{f} |

Rearranging, we get our expression for the gain! | V_{out}/V_{in} = -R_{f}/R_{in} |

__How does this effect the characteristics of an inverting amplifier?__

The gain depends on the ratio of both resistances. If R _{f} is a variable resistor, we can manually change the gain (like a volume knob on a speaker!) | Higher R_{f} means a larger gain (in magnitude, though the sign will be flipped)Lower R _{f} 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__

__Non-inverting amplifier__

__How can you identify a non-inverting amplifier?__

V_{in} 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:

## V_{out}/V_{in} = 1 + R_{f}/R_{1}

**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 V_{in} | V^{+} = V_{in}Thus, V ^{+} = V^{–} = V_{in} |

No current flows through the inputs. At the inverting input, all current must flow between the 2 resistors R _{1} & R_{f} | |

Since R_{1} & R_{f} are in series, the current in them must be EQUAL. | I_{1} = I_{f} |

The total potential difference across R_{1} & R_{f} is V_{out}Now we can consider a potential divider! | V_{1} + V_{f} = V_{out} |

Potential difference across R_{1} can be calculated by considering the potential divider R_{f} & R_{1} | V_{1} = V_{out} x R_{1}/(R_{1} + R_{f}) |

However, we also know that V_{1} is V_{in} as R_{1} is connected between the ground & V^{–} | V_{1} = V_{in}Thus, V _{in} = V_{out} x R_{1}/(R_{1} + R_{f}) |

Rearranging to express gain on one side, | V_{out}/V_{in} = (R_{1} + R_{f})/R_{1} |

Simplifying, we get our expression for the gain! | V_{out}/V_{in} = 1 + R_{f}/R_{1} |

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

The gain depends on the ratio of both resistances. If R _{f} is a variable resistor, we can manually change the gain (like a volume knob on a speaker!) | Higher R_{f} means a larger gainLower R _{f} 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 |