lesson
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If you twist two audio cables together to combine a microphone and a synthesizer into one speaker, the signals do not cleanly add up. Instead, the output impedance of one device loads down the other, distorting both signals and causing nasty crosstalk.
To mix signals without them interfering with each other, professional mixing consoles rely on an elegant circuit trick: the summing amplifier powered by a virtual earth.
How can an active circuit combine multiple independent voltages while keeping each channel completely isolated?
The Virtual Earth Concept
An ideal operational amplifier (op-amp) has near-infinite open-loop voltage gain (AOL→∞) and draws zero input current (Iin=0 A) due to its near-infinite input impedance.
When we connect the non-inverting input (V+) directly to 0 V ground and apply negative feedback through a feedback resistor (Rf), the op-amp continuously drives its output to force the differential input voltage (V+−V−) to zero.
📊Interactive diagram
This creates a virtual earth: the inverting input is held firmly at 0 V by feedback action, even though it has no physical connection to ground. In the 1940s, pioneer John R. Ragazzini and his team formalized this negative feedback behavior while developing operational amplifiers for analog computing.
What happens when we attach multiple independent audio channels to this single virtual earth point?
Summing Multiple Inputs
In an inverting summing amplifier, each input channel (V1,V2,…,Vn) connects through its own input resistor (R1,R2,…,Rn) to the common inverting summing node.
📊Interactive diagram
Because the summing junction sits at a constant 0 V, the current through any input resistor depends solely on its own input voltage: Ik=RkVk−0=RkVk.