Inverting Amplifier

Another useful basic op amp circuit, the inverting amplifier. The triangular gain block symbol is again used to represent an ideal op amp. The input terminal, + (Vp), is called the non-inverting input, whereas – (Vn) marks the inverting input. It is similar to the non-inverting circuit shown in Figure 4 except that now the signal is applied to the inverting terminal via R1 and the non-inverting terminal is grounded.Inverting Amplifier

To understand this circuit, we must derive a relationship between the input voltage, Vi and the output voltage, VO.
Since Vp is tied to ground,
[pmath]Vp = 0 [/pmath]
Remembering that there is no current into the input, the voltage at Vn can be found using superposition. First let VO = 0,
[pmath]Vn = Vi (R2/(R1+R2))[/pmath]
Next let Vi = 0
[pmath]Vn = Vo (R1/(R1+R2))[/pmath]
Combining
[pmath]Vn = Vo (R1/(R1+R2)) + Vi (R2/(R1+R2))[/pmath]

Remembering equation

[pmath]VO = aVd = a(Vp – Vn)[/pmath] substituting and rearranging,

[pmath]A = Vo/Vi = 1-(1/b)1/(1+(1/ab))[/pmath]
where
[pmath]b=R1 /(R1+R2)[/pmath]
Again we have an amplifier circuit. Because b ≤ 1, the closed loop gain, A, is negative, and the polarity of Vo will be opposite to Vi. Therefore, this is an inverting amplifier.