The summer circuit of Fig. 1 has a number of applications. We can sum DC signals, AC signals, logic signals, to any arbitrary waveform that is within the dynamic range of the output of the operational amplifier. We can write a simple formula for the action of the summer circuit:
Vo = - RF * ( (V1 / R1 ) + (V2 / R2) + (V3 / R3) + …)
where the Vi’s can be functions of time as well as Vo. We could also generalize the Ri’s into general impedances Zi’s which could be inductors, capacitors, resistors, or combinations thereof. Discussing all of these possibilities is beyond the scope of our discussion.
We should mention however, that the circuit has a number of possible applications such as mixing different signal frequencies, adding or subtracting bits to a logic sequence, reconstruction of time multiplexed frequencies (frequencies must be within the bandwidth of the op-amp), and other applications that may be imagined.
One interesting application is the mixing of two or more frequencies to form a composite signal. For example if we added 1000 HZ, 2000 HZ, and 3000 HZ sine waves we would get a composite signal whose shape would depend not only on the frequencies but also the amplitudes and phases of the individual signals. If the composite signal is analyzed with a fast Fourier transform (FFT), we would find spectral lines for the different frequencies with the spectral amplitudes relative to each signal strength.
The following equation
Vo = -RF * ( (A1*sin(w1*t+p1) / R1) + (A2*sin(w2*t+p2) / R2 + …)
where the w1, w2, … are the radian frequencies and p1, p2, … are the phases.
One interesting case is when all the frequencies to be added are the same but the phases are different. The sum will be a sine wave with a single frequency equal to the original input frequency, but its phase will be the average of the phases of the original input frequencies if the phase differences are small. But the output signal will of course be inverted. Note however, if two signals of the same frequency but have 180 degrees difference in phase, we will have a cancellation effect for the two signals. Relative signal amplitudes of course will have an effect on the sum.
Vo = - RF * ( (V1 / R1 ) + (V2 / R2) + (V3 / R3) + …)
where the Vi’s can be functions of time as well as Vo. We could also generalize the Ri’s into general impedances Zi’s which could be inductors, capacitors, resistors, or combinations thereof. Discussing all of these possibilities is beyond the scope of our discussion.
We should mention however, that the circuit has a number of possible applications such as mixing different signal frequencies, adding or subtracting bits to a logic sequence, reconstruction of time multiplexed frequencies (frequencies must be within the bandwidth of the op-amp), and other applications that may be imagined.
One interesting application is the mixing of two or more frequencies to form a composite signal. For example if we added 1000 HZ, 2000 HZ, and 3000 HZ sine waves we would get a composite signal whose shape would depend not only on the frequencies but also the amplitudes and phases of the individual signals. If the composite signal is analyzed with a fast Fourier transform (FFT), we would find spectral lines for the different frequencies with the spectral amplitudes relative to each signal strength.
The following equation
Vo = -RF * ( (A1*sin(w1*t+p1) / R1) + (A2*sin(w2*t+p2) / R2 + …)
where the w1, w2, … are the radian frequencies and p1, p2, … are the phases.
One interesting case is when all the frequencies to be added are the same but the phases are different. The sum will be a sine wave with a single frequency equal to the original input frequency, but its phase will be the average of the phases of the original input frequencies if the phase differences are small. But the output signal will of course be inverted. Note however, if two signals of the same frequency but have 180 degrees difference in phase, we will have a cancellation effect for the two signals. Relative signal amplitudes of course will have an effect on the sum.
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