Assignment #12

ECE 2004

Pick four of the five problems below. For all five problems, assume that the op amp is almost ideal where Ri = ∞, Ro = 0 , V+ =10V, and V- = -10V. Watch for the + and – signs on the input terminals of the op amps as the noninverting and inverting input terminals of the op amp are not always in the same orientation in each of the circuits.

  1. Draw the voltage transfer characteristic, Vo vs. Vin, for the inverting amplifier circuit shown below. Note that Vo is the node voltage at the output terminal of the op amp and is also the voltage drop across the dependent voltage source that is part of the op amp model
  2. Let Vin vary from -5V to +5V.
  3. Label the following regions: positive saturation, linear region, and negative saturation.

The op-amp configuration given above constitutes a non-inverting amplifier whose gain is:

This can be proved by applying KCL at the inverting (-) terminal of the opamp:

Rearranging gives:

Thus:

a,b).

  1. A load resistor is attached to the output terminal of the inverting amplifier. The ideal op amp model has been drawn within the symbol for the op amp, which is shown in red. Calculate the currents is, if, i, and iL when Vin = 1V.

Since V1=V2=0 V,

Additionally, no current enters the opamp so that:

From inspection, the output voltage of the inverting amplifier is:

Finally, applying KCL at the output:

Which simplifies to:

In summary:

For Vin=1 V, we have:

  1. Calculate the values for VL, is, if, i, and iL.

Since no current enters the opamp, , and 3 V appears at the non-inverting input of the opamp as depicted above. Since the inverting input (- terminal and also VL) follows the voltage of the non-inverting terminal, VL=3V. Similarly, must also equal 0 A. Next, the configuration above is that of a non-inverting amplifier as in Problem 1(although drawn a little differently). Thus, the voltage at the output of the opamp is:

Finally, In summary:

  1. Determine the output voltage of the op amp, vo.

From inspection, . Now, we can note that is the voltage across the 50 kΩ resistor since the inverting terminal of the opamp is at ground. Thus, . Next, we can apply KCL at V1 to determine the output voltage, Vo.

Substituting in the expression for Iin and rearranging the equation gives:

  1. Determine the value for Is such that:
  2. The amplifier has just entered the positive saturation region.
  3. The amplifier has just entered the negative saturation region.

The opamp is in the non-inverting configuration (in regards to VIN), so that we have:

Furthermore,

Saturation occurs when the ouput reaches the voltage rails of the opamp, ±10V. So, we can write:

a) 1.333 mA. b). -1.333 mA