The circuit shown below is the linear equivalent model of a two-input single-output amplifier. Note that it contains a current dependent voltage source.
Figure 7-1
One application of this amplifier is in a communications circuit where its two inputs are driven by two antennas. We can model the two antennas as two current sources: iIN1 and iIN2, as shown below.
Figure 7-2
The elements in the circuit have the following values: R=3kΩ and rm=3kΩ
Assuming that iN1=1mA and iN2=0A, what is the value of vOUT in Volts?
3
incorrect
Assuming that iN1=0A and iN2=1mA, what is the value of vOUT in Volts?
3
incorrect
Assuming that iN1=1mA and iN2=1mA, what is the value of vOUT in Volts?
3
incorrect
Assuming that Input 2 is left as an open circuit, what is the Thevenin equivalent resistance (in kOhms) seen from Input 1?
6
correct
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To determine the value of vOUT in volts, we need to analyze the circuit and apply the appropriate equations.
First, let's review the given values of the elements in the circuit:
- R = 3kΩ (resistor)
- rm = 3kΩ (internal impedance representing the amplifier)
Now, let's consider the different scenarios and calculate the corresponding vOUT values:
1. Assuming iN1 = 1mA and iN2 = 0A:
To calculate vOUT in this case, we need to find the voltage across the resistor R. Since iN2 is 0A and there is no current flowing through R, the voltage across it will also be 0V. Therefore, vOUT in this scenario will be 0V.
2. Assuming iN1 = 0A and iN2 = 1mA:
Again, to calculate vOUT, we need to find the voltage across the resistor R. Since iN1 is 0A and there is no current flowing through R, the voltage across it will also be 0V. Therefore, vOUT in this scenario will be 0V.
3. Assuming iN1 = 1mA and iN2 = 1mA:
Now we have two identical current sources, both with 1mA. Since these two currents will combine and flow through R, we can consider them as a single current source of 2mA. Therefore, the voltage across R in this case will be (2mA * 3kΩ) = 6V. Hence, vOUT would be 6V.
4. Assuming Input 2 is left as an open circuit:
When Input 2 is left as an open circuit, it means that there is no current flowing into Input 2. In this case, Input 1 will have the full 1mA current flowing through it. The Thevenin equivalent resistance seen from Input 1 is equal to the parallel combination of R and rm. So, the Thevenin equivalent resistance would be:
1 / (1/R + 1/rm)
= 1 / (1/3kΩ + 1/3kΩ)
= 1 / (2/3kΩ)
= 3kΩ / 2
= 1.5kΩ
Therefore, the Thevenin equivalent resistance seen from Input 1 would be 1.5kΩ (or 1500Ω).
To find the value of vOUT in volts, we need to analyze the circuit.
Given that iN1=1mA and iN2=0A, it means that only Input 1 is active and Input 2 is disconnected. Therefore, we can consider Input 2 as an open circuit.
To find vOUT, we can use the superposition principle and consider the contribution of each individual input.
When iN1=1mA and iN2=0A:
Since Input 2 is disconnected, the current source iIN2 can be ignored. Now, we have a simple circuit with only Input 1 and the dependent source.
To find vOUT, we can apply Ohm's Law. The current flowing through R1 will be the same as iIN1, which is 1mA.
Using Ohm's Law, we have:
vOUT = iIN1 * R1
= 1mA * 3kΩ
= 3V
Therefore, when iN1=1mA and iN2=0A, the value of vOUT is 3 volts.