Why −180° matters: Nyquist and margins
Negative feedback can become reinforcing feedback when the returning signal is inverted and strong enough.
First, picture it
The summing junction subtracts the returning signal. If the loop adds another −180° phase shift, subtraction of an inverted signal becomes addition. If its magnitude is also 1, the return can sustain itself. This is why the critical Nyquist point is −1, not simply any point at −180°.
What the model says
For unity negative feedback, the characteristic equation is 1+L(s)=0. On the imaginary axis this can happen at L(jω)=−1: magnitude 1 and phase −180°. Phase margin is the extra phase lag from the gain-crossover phase to −180°: PM=180°+∠L(jωgc) using the appropriate unwrapped branch. Gain margin is 1/|L(jωpc)| at phase crossover, often reported as −20 log₁₀|L(jωpc)| dB. More margin often means more tolerance to uncertainty, but not a universal safety guarantee. With open-loop right-half-plane poles, multiple crossovers, delays or unusual loops, a single margin number is insufficient; use the full Nyquist encirclement criterion and a stated loop definition.
1+L(jω)=0 ⇔ L(jω)=−1; PM=180°+∠L(jωgc)At −180° alone, a loop can still be safely below unity gain. The combined magnitude-and-phase condition matters.
Distance to −1: 0.77. This is a geometric illustration at one frequency, not a stability test for an entire loop.
Make it concrete
At 0 dB crossover, a phase of −135° gives a 45° phase margin under the standard single-crossover convention. An additional 45° of lag would reach the critical direction.
'−180° means unstable' is false. The gain must also be considered, and Nyquist encirclements account for unstable open-loop poles.
Check your understanding+
At phase −180°, is a loop with |L|=0.1 necessarily at the critical point?
No. It is at −0.1, not −1. The standard gain margin there is 10×, or 20 dB, if the usual assumptions apply.