Active Examples
On this page Legacy Designs are compared with Shadow’s Designs. Shadow’s Procedure creates balanced circuits with minimal bias current error. This constraint was not imposed on the Legacy Designs.
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Gain = -5 |
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Legacy Inverting Amplifier |
Shadow |
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Let RF = 100k RI = 100k / 5 = 20k |
Let RF = 100k G0 = 1 - ( -5) = 6 RI = 100k / 5 = 20k R0 = 100k / 6 = 16.67k ZP+ = 16.67k ZP- = 20k // 100k = 16.67k |
For Inverting Amplifiers the main difference
is the ground resistor. Shadow’s procedure automatically adds a resistor
to equalize the impedances seen by the op-amp. Ozzie s Rule
allows R0 to be replaced with a short. This will create a schematic identical
to the Legacy design.
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Legacy |
SHADOW |
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Use Attenuator Plus Buffer R2 / (R1 + R2) = 0.65 Let R1 + R2 = 1k R2 = 650 R1 = 1k - 650 = 350 |
Let RF = 100k G0 = 1 - (0.65) = 0.35 R1 = 100k / 0.65 = 153.85k R0 = 100k / 0.35 = 285.7k ZP+ = 153.85k // 285.7k = 100k ZP- = 100k |
There is no Legacy Circuit for positive gains
less than 1. You can use an attenuator and buffer. Shadow’s procedure
automatically adds a feedback resistor for balance. The feedback resistor can
be shorted by using Ozzie
s Rule.
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Gain = 5 |
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Legacy Non-Inverting Amplifier |
Shadow |
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1 + RF / RI = 5 RF / RI = 4 Let RF = 100k RI = 100k / 4 = 25k |
Let RF = 100k G0 = 1 - ( 5) = -4 R1 = 100k / 5 = 20k R0 = 100k / 4 = 25k ZP+ = 20k ZP- = 25k // 100k = 20k |
Shadow’s procedure adds R1. Ozzie s Rule says you can replace R1 with a short.
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Legacy Inverting Summer |
Shadow |
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Let RF = 100k RI1 = 100k / 5 = 20k RI2 = 100k / 7 = 14.29k |
Let RF = 100k G0 = 1 - ( -5 -7) = 13 Rn1 = 100k / 5 = 20k Rn2 = 110k /7 = 14.29k R0 = 100k / 13 = 7.69k ZP+ = 7.69k ZP- = 20k // 14.29k // 100k = 7.69k |
R0 can be shorted via Ozzie s Rule to get the same circuit.
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Gains = 5, 7 |
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Legacy |
Shadow |
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V(out) / V+ = 1 + RF / RI Via superposition (R2 / (R1 + R2)) * (1 + RF / RI) = 5 (R1 / (R1 + R2)) * ( 1 + RF / RI ) = 7 Solve above equations Reader exercise |
Let RF = 100k G0 = 1 - ( 5 + 7) = -11 Rp1 = 100k / 5 = 20k Rp2 = 100k / 7 = 14.29k R0 = 100k / 11 = 9.09kk ZP+ = 20k // 14.29k = 8.33k ZP- = 9.09k // 100k = 8.33k |
The Legacy procedure requires some equations
to be solved. Positive gain summing
circuits are very interactive. Changing
any component value will affect all gains.
Due to this interaction and the design complexity, they are rarely used.
Shadow’s procedure hides this. The number of inputs does not change the procedure. Each input needs an input resistor. The values are calculated via Rf/gain. A ground resistor is added to make the gain add to one.
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Gains = +2, +3, -4 |
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Legacy |
Shadow |
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The equations are rather complex. Design is left as a reader exercise |
Let RF = 100k G0 = 1 - ( 2 + 3 - 4) = 0 Rp1 = 100k / 2 = 50k Rp2 = 100k / 3 = 33.3k Rn = 100k / 4 = 25k ZP+ = 50k // 33.3k = 19.99k ZP- = 25k // 100k = 20k |
With Legacy Analysis there is no way to
determine the circuit. Does it need a ground resistor on the "+"
input, the "-" input, or none?
You could use ground resistors on both inputs, but this will reduce
circuit performance. To avoid this you
need to try all 3 cases. Most texts
consider this to be too difficult and recommend a two op-amp solution.
Shadow’s Procedure hides the complexity. The ground gain step determined that no ground resistor was needed. The input resistors are easily calculated. The discrepancy between ZP+ and ZP- is due to round off error.
Summary & Conclusion
For simple circuits, the Legacy Analysis needs fewer steps than the Shadow procedure, no validity check
Shadow’s procedure creates a balanced circuit
with minimal bias current error. You can use Ozzie 's Rule to remove resistors that are only needed
for a balanced design.
Shadow adds the minimum amount of ground gain to optimize circuit performance.
For a circuit with multiple positive gains or mixed gains, Shadow’s procedure is far simpler than Legacy Analysis. Many texts consider the design of mixed gain single op-amp summing circuits too difficult to handle.
The main advantage of Shadow’s
procedure is that the same procedure works for all cases.
For the designer that occasionally hits the wrong key on his calculator, a simple check is included in the Shadow procedure.