Frequency counter behavior at high input frequencies In a digital frequency counter, what typically happens when the input frequency is very high and the sampling (gate) interval is chosen too long relative to the counter's register capacity and design limits?

Introduction / Context:
A frequency counter counts the number of input cycles during a fixed gate (sampling) interval, then computes frequency as counts / gate_time. At very high input frequencies, the number of pulses during a long gate can exceed the counter’s register capacity, leading to overflow. Understanding this limitation is essential when selecting gate times and counters for RF or high-speed digital measurements.

Given Data / Assumptions:

• Counter measures frequency by counting input edges over a fixed gate time.
• The counter uses a finite-width register (for example, 24 or 32 bits).
• Input frequency can be high enough that counts in a long gate exceed the register’s maximum value.
• No prescaler or divide-by-N front-end is assumed unless stated.

Concept / Approach:
Let N_max be the maximum count a register can hold. During a gate time T_g, the expected count is N = f_in * T_g. If N > N_max, the digital counter wraps around (overflow), producing an invalid reading. Designers mitigate this by shortening T_g, adding a prescaler, or using reciprocal counting methods at high frequencies.

Step-by-Step Solution:
Define capacity → N_max determined by register width.Compute expected count → N = f_in * T_g.Compare → if N > N_max, overflow occurs.Conclusion → With too long T_g at very high f_in, the counter overflows.

Verification / Alternative check:
Check the specified maximum frequency without prescaling for a chosen gate time. Many instruments also provide overflow indicators or error flags when the count exceeds capacity.

Why Other Options Are Wrong:

• The counter works fine: ignores finite register limits.
• Undercounts: long gate typically increases counts; overflow, not undercount, is the failure mode.
• Less precise: long gates usually increase precision; precision loss is not the primary issue here.

Common Pitfalls:
Assuming longer gate time is always better. At high frequencies, use prescalers or shorter gates to prevent overflow.

Final Answer:
The counter overflows.