February 16, 1998

Feedback made simple--continued

I once designed an oscillator that didn't always oscillate. It was so sensitive that the frequency would change when I got near it!

In my last column ("Feedback made simple," EDN, Jan 15, 1997, pg 24), I established that the loop gain, Agreek beta, lc, determines stability per the feedback equation below. If the loop gain achieves a magnitude of one and the phase shift equals ­180°, the denominator of the feedback  equation goes to zero.

Liberally interpreted, the gain goes to infinity and explodes our world, but energy-limited power supplies save us. Any one of three things happens now. "Lockup" is a state that occurs when the circuit output goes to a power rail and stabilizes. A second possibility is that a sine-wave oscillator forms because the amplifier gain decreases as its output approaches a power rail, causing stable operation. Residual charge pushes the output past the stable point, and, as the output swings away from the rail, the gain increases until the circuit becomes unstable. A third possibility occurs in a limit cycle. In this cycle, the loop gain and the residual charge are high, and the output crashes into the rails, causing a square-wave output. This summation provides a classic, nontextbook definition of oscillation.

I once designed an oscillator that didn't always oscillate. When it oscillated, the frequency was wrong, and the output was distorted under some conditions. It was so sensitive that the frequency would change when I got near it! Thus, because my philosophy is "when all else fails, read the directions or try theory," I broke the loop and calculated Agreek beta,lc. The calculated magnitude of the loop gain at the center frequency was 4V/V, and the phase shift was ­180°; the circuit should oscillate. To verify the theory, visiting the lab is the next step.

In the lab, an amplifier Bode plot showed ­240° phase shift at the center frequency; the phase shift was ­180° at the center frequency÷2, so it oscillated there. If the loop gain equals one, a circuit oscillates when the phase shift reaches ­180°. Transistors have appreciable phase shift at f_t/50, Miller effect introduces phase shift, and stray capacitance from long leads varies. The early accumulation of phase shift accounts for the oscillation at the center frequency÷2. The variable wiring capacitance caused flaky performance, such as unreliable start-up and unpredictable frequency variations. The circuit oscillated at the center frequency with a redesigned amplifier, but the output was still distorted, and the center frequency was unstable.

The amplifier gain measured 10V/V, and the feedback-network gain measured 0.35V/V; these measurements resulted in a loop gain of 3.5V/V. After I reduced the amplifier gain to 4V/V, the output distortion disappeared. Further amplifier-gain reductions can improve distortion performance, but the circuit might not oscillate under worst-case conditions. The final problem with the original circuit was frequency instability.

The phase-shift rate of change, dgreek phi,lc/dt, determines the frequency drift. The oscillator frequency and its stability are a design challenge, because the phase shift in most circuits is a highly nonlinear, tangential function. I redesigned the feedback network to get a better dgreek phi,lc/dt by positioning the center frequency on the sharp slope of the tangent function. The frequency stability improved, and I was a happy camper.

My next column deals with methods for troubleshooting electronic equipment. I will start with a systems approach for ensuring success, and, if the interest is there, I can get into specific techniques in a future column.

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