Operational Amplifiers

The Basic Ideal Op-Amp Analysis Strategy

For any Ideal Op-Amp with negative feedback you may assume:
• V^- = V⁺ (But not necessarily 0)
• I^- = I⁺ = 0
• Now write KCL equations everywhere except at V-sources and the Op-Amp output.
• Do some algebra to find your answer
• Since the output voltage can not exceed the power supplies, check to see that

  V_PS- < V_O < V_PS+

The Inverting Amplifier Configuration

Figure 1.

Let's find V_O = f(V_S)

KCL at V^-:

(V^- - V_S) /R₁ + (V^- - V_O) /R_F = 0

Note that in this case V⁺ = 0! So,

V^- = V⁺ = 0. So,

V_O = -(R_F /R₁)V_S. Note that the value of R_L does not matter!

Let V_S be a triangle wave with peaks at +2 and -2. See Figure 2. Let
R_F = 6K and
R_F = 2K. So,

V_O = -(6K / 2K)V_S is an "upside down" triangle 3 times taller than V_S. So, the peaks of V_O are at +6 and -6. See Figure 2.

If V_PS- = -10 Volts and V_PS+ = +10 Volts then the output voltage V_O is well within the power supply limits and linear amplification does indeed take place as seen in Figure 2.

Figure 2.

Now let V_S be a triangle wave with peaks at +2 and -2. See Figure 3. Let
R_F = 12K and
R_F = 2K. So,

V_O = -(12K / 2K)V_S is an "upside down" triangle 6 times taller than V_S. So, the peaks of V_O should be at +12 and -12.

But If V_PS- = -10 Volts and V_PS+ = +10 Volts then the output voltage V_O tries to exceed the power supply limits. When the output tries to go beyond the power supply limits we say that the op-amp is "in saturation." Linear amplification does not take place when the op-amp is in saturation. Output values are "clipped" at the supply values as seen in Figure 3.

Figure 3.

The Summing-Inverter Configuration

Figure 4.

Since the circuit in Figure 4. has negative feedback the above assumptions are true.

Let's find V_O = f(V₁, V₂)

KCL at V^-:

(V^- - V₁) /R₁ + (V^- - V₂) /R₂ + (V^- - V_O) /R_F = 0

Note that since the current I⁺ = 0 then there is no voltage across R_X ! So, V⁺ = 0

But V^- = V⁺ = 0 So,

V_O = -[(R_F /R₁)V₁ + (R_F /R₂)V₂)]

The Non-Inverting Configuration

Figure 5.

Since the circuit in Figure 5 has negative feedback the above assumptions are true.

(V^- - 0) /R₁ + (V^- - V_O) /R_F = 0

But V^- = V⁺ = V_S So,

V_O = (R_F /R₁ + 1)V_S

The Voltage Follower Configuration

Figure 6.

Since the circuit in Figure 6. has negative feedback the above assumptions are true.

By inspection

V_O = V^- = V⁺ = V_S

We say that the output voltage follows the input voltage. They are in phase and have the same magnitude.

The Differential Configuration

Figure 7.

Can you show that

V_O = [(R_F /R₁) + 1)*(R_X /(R_X + R_Y))]V_S2 - [R_F /R₁]V_S1 ??

Note that if all the resistors are the same value then

V_O = V_S2 - V_S1 !

Finding the Output Current I_O

Figure 8.

Find V_O first using the same procedures as in the inverting amplifier configuration. Then find I_O by writing a KCL equation at V_O using the KNOWN VALUE of V_O and V^- that you just calculated.

KCL at V_O:

I_O = (V_O - V^-) /R_F + V_O /R_L

Note that since the current I⁺ = 0 then there is no voltage across R₂ ! So, V⁺ = 0

Practice Problem

Can you find V_O = f(V_S) for the circuit in Figure 9?

Figure 9.

End Operational Amplifiers Page

Last modified: Sun Oct 22 13:37:58 2000