Im trying to understand this basic circuit from a book.
The book said:
"The analysis is simple, if you remember your golden rules:
(The golden rules:
I. The output attempts to do whatever is
necessary to make the voltage difference
between the inputs zero.
II. The inputs draw no current. )
- Point B is at ground, so rule I implies that point A is also.
-
This means that (a) the voltage across R2 is VOut and (b) the voltage across R1 is Vin"
-
So, using rule 11, we have
In other words,
voltage gain = Vout/Vin = -R2/R1
I cant understand why voltage across R1 is Vin and in R2 is Vout
Best Answer
Because the inverting (-) input is at 0V (a virtual ground), the voltage across R1 is:
$$V_{in} - 0 = V_{in}$$
By the same reasoning, the voltage across R2 is:
$$V_{out} - 0 = V_{out}$$
The thing that might not be so obvious is that if \$V_{in}\$ is positive, \$V_{out}\$ will be negative. In that case the current flows straight from \$V_{in}\$ to \$V_{out}\$, passing through R1 and R2. The inverting input draws no current, so all current must flow from in to out, and through the resistors.
So as an example, say \$V_{in}\$ is 1V, R1 is 100Ω and R2 is 200Ω. Then \$V_{out}\$ will be -2V by your formula, the difference between \$V_{in}\$ and \$V_{out}\$ is 3V, dropped across a total of 300Ω, gives a current of 10mA from in to out through R1 and R2.