An ideal op amp by itself is not a very useful device since any finite input signal would result in infinite output. By connecting external components around the ideal op amp, we can construct useful amplifier circuits. Figure 4 shows a basic op amp circuit, the non-inverting amplifier. The triangular gain block symbol is used to represent an ideal op amp. The input terminal marked with a + (Vp) is called the non-inverting input; – (Vn) marks the inverting input.
To understand this circuit we must derive a relationship between the input voltage, Vi, and the output voltage, VO.
Remembering that there is no loading at the input,
Vp = Vi
The voltage at Vn is derived from VO via the resistor network, R1 and R2, so that,
[pmath]Vn = V o R1 / (R1+R2) = Vo b[/pmath]
[pmath]b= R1 / (R1+R2)[/pmath]
The parameter b is called the feedback factor because it represents the portion of the output that is fed back to the input.
Recalling the ideal model,
[pmath]VO = aVd = a(Vp – Vn)[/pmath]
[pmath]VO = a(Vi – bVO)[/pmath]
and collecting terms yield,
[pmath]A =Vo/Vi =(1/b)1/(1+1/ab)[/pmath]
This result shows that the op amp circuit of Figure 4 is itself an amplifier with gain A. Since the polarity of Vi and VO are the same, it is referred to as a non-inverting amplifier.
A is called the close loop gain of the op amp circuit, whereas a is the open loop gain. The product ab is called the loop gain. This is the gain a signal would see starting at the inverting input and traveling in a clockwise loop through the op amp and the feedback network.