A summing amplifier, also known as an op-amp summing amplifier, is an electronic circuit that combines multiple input signals and produces an output signal that is proportional to the sum of these inputs. It's commonly used in various applications such as audio mixing, signal processing, and control systems. The core component of a summing amplifier is the operational amplifier (op-amp), a high-gain voltage amplifier.
The basic configuration of a summing amplifier involves an op-amp and multiple input resistors connected to the inverting input terminal of the op-amp. Each input signal is connected through a resistor, and these resistors determine the individual contribution of each input to the final output. The op-amp's output is then taken from its output terminal.
Here's a simplified explanation of how a summing amplifier combines inputs:
Op-Amp Behavior: Op-amps are designed to maintain a virtual short circuit (zero voltage difference) between their inverting (-) and non-inverting (+) inputs. In a summing amplifier, the inverting input is typically used, and this principle is applied.
Input Contributions: Each input signal is connected through a resistor to the inverting input of the op-amp. The resistor values determine the gain or scaling factor for each input. The larger the resistor value, the smaller the contribution of that input to the overall sum.
Superposition Principle: According to the superposition principle, when several inputs are applied to a linear circuit, the response at any output point is the algebraic sum of the responses that would be produced if each input were applied individually, while all other inputs are turned off.
Voltage Division: The input resistors create a voltage division network. The voltage at the inverting input terminal of the op-amp is the weighted sum of the voltages across these resistors (based on their values and the input voltages). This voltage is then amplified by the op-amp's gain.
Output Calculation: The op-amp amplifies the voltage difference between its inputs with a very high gain. Since the inverting input is held at a virtual ground (due to the op-amp's behavior), the output voltage will be proportional to the sum of the input voltages, taking into account the gain factors associated with each input.
Mathematically, the output voltage (
out
V
out
) of a summing amplifier can be expressed as:
out
=
−
(
1
⋅
1
+
2
⋅
2
+
…
+
⋅
)
V
out
=−(
R
1
R
f
⋅V
1
+
R
2
R
f
⋅V
2
+…+
R
n
R
f
⋅V
n
)
Where:
R
f
is the feedback resistor connected between the output and the inverting input of the op-amp.
1
,
2
,
…
,
R
1
,R
2
,…,R
n
are the input resistors.
1
,
2
,
…
,
V
1
,V
2
,…,V
n
are the input voltages.
In practical designs, care must be taken to choose appropriate resistor values to achieve the desired input scaling and output range.