Tutorial 7 D - The Inverting Amplifier

Learning Objectives

• use the formula voltage gain = Vout/Vin

• recall and use the definition of bandwidth of an amplifier as the frequency range over which the voltage gain is within 70% of the maximum;

• draw and recognise the inverting op-amp amplifier circuit and describe its applications;

• use the formula Vout = – Rf

•                            Vin      Rin

• recall that the input resistance is equal to the value of the input resistor, and that the circuit has a virtual earth point;

Negative feedback is achieved by bringing a fraction of the output signal to the inverting input of the op-amp.   The photograph shows an op-amp with negative feedback to give an inverting amplifier. Negative feedback also has the following effects:

• The gain is reduced

• The bandwidth (frequency response) is increased

• The stability is improved.

This allows the op-amp to be used in many applications including audio.

The diagram shows a typical negative feedback arrangement: In this arrangement the non-inverting input is connected to the 0V line.  Since there is very little voltage difference between the non-inverting and the inverting input, we can also say that the voltage at the inverting input is almost at 0V as well. So we say that the inverting input is at a virtual earth.

 Question 1 Explain in terms of the difference between the inputs of the amplifier what is meant by a virtual earth? Let us suppose there is a current I1 flows through Ra and a current I2 flows through Rf.  Ohm’s Law allows us to say:

• Current through Ra,

I1 = Vin/Ra

• Current through Rf,

I2 = Vout/Rf

Since the resistance at the inverting terminal is very high, no current can flow through the inverting input.  At point X (according to Kirchhoff I) the current in is the same as the current out.  Therefore the current is the same through Ra and Rf. • Kirchhoff I:

I1 + I2 = 0

• Substituting:

Vin/Ra  +  Vout/Rf = 0

• Rearranging:

Vin /Ra = - Vout/Rf

• Therefore:

Vout / Vin = - Rf/Ra

Since point X is at a virtual earth and the voltage of X is zero, and therefore the input resistance is the same as the input resistor.  So the input resistance of this amplifier is 1000 W.  This will have implications for load matching for an input device such as a microphone.  The output in all inverting amplifiers relates to the input as shown below: Note the input and output are 180 degrees out of phase.

 Question 2 If  Ra = 1000 W and Rf = 100000 W, what is the gain of the inverting amplifier?  Summary The Inverting Op-amp uses negative feedback; Inverting input is a virtual earth. Links Electronics-Tutorials WISC online presentation Video Tutorial