Why Feedback Loops are Essential in Flip-Flops for Stable Memory Storage

Feedback loops are a critical component in flip-flops, ensuring the stability and reliability of memory storage in digital systems. These feedback mechanisms play a vital role in preventing the instability that can occur when the outputs of memory elements change while the outputs of the combinational circuit connected to the flip-flop inputs are being sampled by the clock pulse. This instability can lead to glitches or incorrect output states, ultimately resulting in data corruption or other issues in the digital system.

Ensuring Stable Input Conditions

To maintain stable memory storage, it is essential that the input to the flip-flop remains stable for a specific duration before and after the clock edge. This duration is known as the setup time (t_su) and hold time (t_h), respectively. These timing requirements are specified in the data sheet for the flip-flop device and are typically in the range of a few nanoseconds to a few hundred picoseconds for modern devices.

The Role of Feedback Loops

Feedback loops in flip-flops help ensure that the inputs to the flip-flop are stable during these critical time periods. The feedback path allows the output of the flip-flop to be fed back to the input, helping to maintain the stability of the output even when the inputs to the combinational circuit are changing.

Example: T Flip-Flop

One example of a feedback loop in a flip-flop is the T flip-flop. In this type of flip-flop, the output state toggles whenever the T input is high and the clock input is strobed. This “divide by” feature has applications in various digital counter circuits.

Challenges in Meeting Timing Requirements

However, it is not always possible to meet the setup and hold time criteria, especially in real-time systems where the flip-flop may be connected to a signal that can change at any time, outside the control of the designer. In such cases, the designer’s goal is to reduce the probability of error to an acceptable level, depending on the required reliability of the circuit.

Theorem: Stable Flip-Flop Output

The stability of a flip-flop can be described by the following theorem:

If the input to a flip-flop is stable for a time greater than or equal to the setup time before the clock edge and the hold time after the clock edge, then the output of the flip-flop will be stable and correct.

Electronics Formulas and Examples

Formula:
* Setup time (t_su) and hold time (t_h) are specified in the data sheet for the flip-flop device and are typically between a few nanoseconds and a few hundred picoseconds for modern devices.

Example 1:
* Consider a flip-flop with a setup time of 10 nanoseconds and a hold time of 5 nanoseconds. If the input to the flip-flop changes 5 nanoseconds before the clock edge and remains stable for 15 nanoseconds after the clock edge, then the output of the flip-flop will be stable and correct.

Example 2:
* A flip-flop has a setup time of 20 nanoseconds and a hold time of 10 nanoseconds. If the input to the flip-flop changes 15 nanoseconds before the clock edge and remains stable for 25 nanoseconds after the clock edge, the output of the flip-flop will be stable and correct.

Flip-Flop with Feedback Loop Diagram

Data Points

• Setup time: 10 nanoseconds
• Hold time: 5 nanoseconds
• Input stability time: 20 nanoseconds
• Output stability time: 30 nanoseconds

Values

• Clock frequency: 100 MHz
• Data rate: 50 Mbps

Measurements

• Setup time measurement: Using an oscilloscope, measure the time between the input changing and the clock edge.
• Hold time measurement: Using an oscilloscope, measure the time between the clock edge and the input becoming stable.

References

1. “Digital Electronics & Computer Design” by M.M. Mano
2. “Flip Flop Basics – Types, Truth Table, Circuit, and Applications” at Electronics for You
3. “Flip-flop (electronics)” at Wikipedia
4. “Feedback and Flip-Flops” at Computer Systems Fundamental
5. “Sequential Logic Circuits and the SR Flip-flop” at Electronics Tutorials