Operational Amplifier Circuit

In summary, the question asks to find the time rate of change of the output for the given circuit after the switch opens. The offset current for the LM353 op-amp is 50 pA and the ideal conditions for the op-amp are i+ = i- and v+ = v-. Using the equation dV+/dt = 5 V/s, the time rate of change of the output can be calculated as dV/dt = 5 V/s when the gain of the op-amp is large.
  • #1
swuster
42
0

Homework Statement


Look up the offset current for the LM353 op-amp and predict the time rate of change of the output for the circuit below after the switch opens. (Find dVo/dt)

opamp.jpg


Homework Equations


offset current = 50 pA
i+ = i-, ideally
v+ = v-, ideally

The Attempt at a Solution


I really don't know where to begin. Vo = V- in this case, so I think the 50 pA are flowing through the other branch. When the switch is flipped, the capacitor discharges, losing voltage. But how can I derive dV/dt when ideal op-amps have infinite gain?

[edit] Had some more insight on this, but still want to check to see if it's right:
If the gain of the op amp is A:

I = C dV(+)/dt
dV+/dt = 5 V/s

Vo = A(v+ - v-) = A(v+ - Vo)
Vo = v+ * A / (1 + A)
dV0/dt = dv+/dt * A / (1 + A)

If A is large then A / (1 + A) = 1 so dV/dt = 5 V/s.
 
Last edited:
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  • #2
Looks good!

(I'll take your word for it on the 50 pA spec.)
 
  • #3


Your approach is on the right track. To find the time rate of change of the output, we can use the concept of virtual ground, which states that the voltage at the inverting terminal (V-) of an op-amp is equal to the voltage at the non-inverting terminal (V+). This means that when the switch is closed, the voltage at V- is equal to the voltage at V+, which is 5V.

When the switch is opened, the capacitor will start to discharge through the resistor, causing a decrease in voltage at V-. This decrease in voltage will cause the output voltage (Vo) to decrease as well. We can use the equation for current in a capacitor (I = C*dV/dt) to find the rate of change of the voltage at V-.

Since the offset current (i+) is flowing through the other branch, we can write the equation for the current flowing through the capacitor as:

I = i+ + C*dV-/dt

Substituting in the value for the offset current (50 pA) and rearranging for dV-/dt, we get:

dV-/dt = (I - i+)/C = (-50 pA)/C

Since the input voltage (V+) is constant at 5V, we can use the formula for the output voltage of an inverting op-amp circuit (Vo = -A*V+) to find the rate of change of the output voltage:

dVo/dt = -A*dV+/dt = -A*5 V/s

Substituting in the value for A (which is large for an ideal op-amp), we get:

dVo/dt = -A*5 V/s = -5 V/s

So, the time rate of change of the output voltage after the switch opens is -5 V/s.
 

1. What is an operational amplifier circuit?

An operational amplifier circuit, or op amp, is an electronic device that amplifies an input signal to a higher level. It is commonly used in electronic circuits to perform mathematical operations, such as addition, subtraction, and differentiation.

2. How does an operational amplifier circuit work?

An op amp consists of a differential amplifier, which amplifies the difference between two input signals, and a gain stage, which amplifies the output of the differential amplifier. The output is then fed back to the input through a feedback loop, which allows for precise control of the output signal.

3. What are the key components of an operational amplifier circuit?

The key components of an op amp circuit include the differential amplifier, gain stage, feedback loop, power supply, and input and output terminals. Some circuits may also include additional components, such as capacitors and resistors, to improve performance.

4. What are the applications of operational amplifier circuits?

Op amp circuits have a wide range of applications in electronics, including audio amplifiers, signal conditioning, filters, oscillators, and voltage regulators. They are also commonly used in instrumentation and control systems.

5. How do I choose the right operational amplifier circuit for my application?

When choosing an op amp circuit, there are several factors to consider, including the required gain, input and output voltage ranges, bandwidth, and power supply requirements. It is also important to consider the op amp's input and output impedance, as well as its noise and distortion characteristics, to ensure optimal performance for your specific application.

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