Question

You are given a cross-coupled inverter pair in which all nodes are set to Vcc/2. Why will this configuration always move to a more stable state?

Answer 1

The Circuit configuration shown in figure is called Cross-coupled inveter pair.

In this circuit if the input of U1 starts with a value of 1, it will produce an output of Q=0. This output is fed back to the input of U2, thus producing an output of Qn=1. Qn is fed back to the original input of U1, thus reinforcing the initial condition. This circuit will hold, or store, a logic 0 without being driven by any other inputs. This circuit operates in a complementary manner when the initial value of U1 is 0. With this input condition, the circuit will store a logic 1 without being driven bt any other inputs.

The cross-coupled inverter pair exhibits metastable behaviour due to its positive feedback configuration. Metastability refers to when a system can exist in a state of equilibrium when undisturbed but can be moved to a different, more stable state of equilibrium when sufficiently disturbed.The cross-coupled inverter pair is a highly metastable system.

This system actually contains three equilibrium states. The first is when the input of U1 is exactly between a logic 0 and logic 1 i.e Vcc/2. In this state, the output of U1 is also Vcc/2. This voltage is fed back to the input of U2, thus producing an output of exactly Vcc/2 of U2. This in turn is fed back to the original input on U1 reinforcing the initial state. Despite this system being at equilibrium in this condition, this state is highly unstable.  With minimal disturbance to any of the nodes within the system, it will move rapidly to one of two more stable states The two stable states for this system are when Q = 0 or when Q = 1. Once the transition begins between the unstable equilibrium state toward one of the two more stable states, the positive feedback in the system continually reinforces the transition until the system reaches its final state. In electrical systems, initial disturbance is caused by the presence of noise and since noise s present in every electrical system so the cross-coupled inverter pair will never be able to stay in the unstable equilibrium state where all nodes are at Vcc/2.

Now let's Examining metastability - moving towards the state Q=0 as shown below. Similiarly we can examine metastability when moving towards the state Q=1.