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Example 7
1.6 kΩ
400 Ω
_
2 kΩ
1.5 kΩ
+
3 kΩ
_
+
+
vo
2V
+
_
_
Calculate v o .
The circuit has two operational amplifiers. For the first op amp, the inverting terminal is
connected to ground through a 400Ω resistor and a feedback resistor is connected
between the inverting terminal and the output node. The output voltage of the first op
amp becomes one of the input voltages of the second op amp. We want to find the output
voltage of the second op amp.
Firstly we need to determine the output voltage of the first op amp, which can be labeled
as v1 . There is zero voltage across the two input terminals of the ideal op amp. So the
inverting terminal voltage should be equal to that of the non inverting terminal. That is
2V. The input currents should be zero for both of the input terminals. The current flow
through the 400Ω resistor is the same as that through the 1.6kΩ resistor. The current
passes the 400Ω resistor is the voltage drop across that divided by the resistance. That is
two volts minus 0, and then divided by 400Ω. The current flows through the 1.6kΩ
resistor is the output voltage of the op amp subtracted by 2, and divided by 1.6kΩ. We
got
v 2
2
 1
400 1600
Both sides of the equation are multiplied by 1600, we get,
8  v1  2
So v1  10V .
The 10V is connected to the second op amp through a 2kΩ resistor.
Voltages at the two input nodes are equivalent. So the voltage for the inverting node
should be 0V since inverting node is grounded.
Apply KCL at the inverting node of the input, we got
v
10
2

 o 0
2k 1.5k 3k
Solve for v o  3k  
10
 2k

2 
  19V
1.5k 