Non-ideal Op-amp Parameters

So far we’ve been operating using some ideal Op-amp Assumptions. Things can be different in real life.

Open-loop Differential Gain

This is called $A_o$ or $A_{\text{diff}}$. It’s defined as:

$$A_{\text{diff}}=\frac{V_o}{V_{in}}=\frac{V_o}{V_{+}-V_{-}}\approx 100\text{K}-1\text{M}\left[\frac{V}{V}\right]$$

Common Mode Gain

If we apply a voltage that is common to both terminals, we actually get some output, such that $V_o$ is a function of $V_{CM}$. (“CM” means “common mode”, as in common to both inputs).

In an ideal scenario, adding a common voltage to the two nodes shouldn’t make a difference. However, there is always going to be a slight difference. If I add some voltage to one side and there is this slight difference, it will seem like I just applied a positive difference to it even though I didn’t. The reason is that transistors are highly reactive.

Governed by:

$$A_{CM}=\frac{V_o}{V_{CM}}$$

This value tends to be many orders of magnitude smaller than $A_{\text{diff}}$.

Common Mode Rejection Ratio

We can quantify the effect of common-mode gain by using a CMRR. In general terms, a rejection ratio is:

$$\text{"Rejection Ratio"}=\frac{\text{Gain we want}}{\text{Gain we don’t want}}$$

For CMRR, this is:

$$\text{CMRR}=\frac{|A_{\text{diff}}|}{|A_{CM}|}[\text{dB}]$$

This is usually in units of decibels.

DC Offset

If we apply $V_{in}=V_{+}-V_{-}=0\text{V}$, you do not get $V_o=0\text{V}$ due to manufacturing randomness.

We use the concept of $V_{\text{OS}}$, defined as:

$$\begin{array}{rl}{V}_{\text{OS}}& =\text{Input-referred offset voltage}\\ & =\text{What }{V}_{in}\text{ is required on average to cancel the offset error}\end{array}$$

Slew Rate

Slew rate refers to how fast an output can change in response to a step input $[\text{V}/\mu s]$? Did this in Lab 1.

Gain Bandwidth Product

This refers to a tradeoff gain to achieve higher frequencies, such that:

$$\text{GBWP}=A_o{f}_o=A_1{f}_1$$