Passive RC circuit produces gain

Could a simple passive RC network without any transformers, inductors, switches, or non-linear components produce a voltage gain?

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Well, it’s not “free energy,” however, yes, and can even use the same value resistor and capacitor in a ladder network shown in Figure 1, although differing values also can be utilized.

Figure 1 Passive RC circuit using resistors and capacitors of the same value in a ladder network.

Of course, this isn’t of much use other than a curiosity, but it’s a fun circuit to build and play around with!

I built one with seven sections (Figure 2) using an R of 10 kΩ and a C of 0.1 µF, then plotted the results.

Figure 2 A seven-section RC ladder network with an R of 10 kΩ and C of 0.1 µF.

The Bode plot can be seen in Figure 3. As you can see, the gain remains around 0 dBv and behaves as a low-pass filter, then slowly rises to a peak of 1.07 dBv at 1 kHz before falling off.

Figure 3 Bode plot of the passive RC circuit showing low-pass filter behavior until a slow rise to a peak of 1.07 dBv at 1 kHz.

This agrees well with the simulation shown in Figure 4.

Figure 4 Circuit simulation of a passive RC circuit that closely matches the Bode plot shown in Figure 3.

If you swap the resistors and capacitors, the circuit behaves like a high-pass filter and produces a higher gain of 1.13 dBv at 26 Hz, as shown in Figure 5, and a simulation in Figure 6.

Figure 5 Bode plot of the passive RC circuit showing high-pass filter behavior.

Figure 6 Circuit simulation of a passive RC circuit that closely matches the Bode plot shown in Figure 5.

As noted by someone, this technique can be employed with an emitter-follower, which has a voltage gain less than unity to create an oscillator. However, that’s for another upcoming Design Idea (DI), which will also include a note on how a single unbiased JFET can produce a +dBv voltage gain!

Anyway, hopefully some folks find this interesting and have some fun!

Michael A Wyatt is a life member with IEEE and has continued to enjoy electronics ever since his childhood. Mike has a long career spanning Honeywell, Northrop Grumman, Insyte/ITT/Exelis/Harris, ViaSat, and retiring (semi) with Wyatt Labs. During his career, he accumulated 32 US Patents and, in the past, published a few EDN Articles, including Best Idea of the Year in 1989.

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