Gain With Feedback At Mid And High Frequency Calculator

Gain with Feedback Formula:

\[ A_f = \frac{\frac{A_m}{1 + (A_m \cdot \beta)}}{(1 + \frac{s}{\omega_{hf}}) \cdot (1 + (A_m \cdot \beta))} \]

Mid Band Gain (A_m):

unitless

Feedback Factor (β):

unitless

Complex Frequency Variable (s):

Upper 3-dB Frequency (ω_hf):

Gain with Feedback (A_f):

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1. What is Gain with Feedback at Mid and High Frequency?

Gain with feedback at mid and high frequency describes the performance of a feedback amplifier system across different frequency ranges, accounting for both the mid-band gain characteristics and the high-frequency roll-off behavior of the amplifier.

2. How Does the Calculator Work?

The calculator uses the gain with feedback formula:

\[ A_f = \frac{\frac{A_m}{1 + (A_m \cdot \beta)}}{(1 + \frac{s}{\omega_{hf}}) \cdot (1 + (A_m \cdot \beta))} \]

Where:

\( A_f \) — Gain with feedback (unitless)
\( A_m \) — Mid band gain (unitless)
\( \beta \) — Feedback factor (unitless)
\( s \) — Complex frequency variable (Hz)
\( \omega_{hf} \) — Upper 3-dB frequency (Hz)

Explanation: This formula accounts for both the feedback effect on the mid-band gain and the frequency-dependent behavior of the amplifier at higher frequencies.

3. Importance of Gain with Feedback Calculation

Details: Calculating gain with feedback is essential for designing stable amplifier circuits, predicting frequency response, and ensuring proper system performance across the operating frequency range.

4. Using the Calculator

Tips: Enter mid band gain and feedback factor as unitless values, complex frequency variable and upper 3-dB frequency in Hz. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the feedback factor?
A: The feedback factor determines how much of the output signal is fed back to the input, affecting stability, bandwidth, and gain characteristics of the amplifier.

Q2: How does frequency affect gain with feedback?
A: At higher frequencies, the gain decreases due to the amplifier's inherent frequency limitations, which is accounted for in the formula.

Q3: What is the typical range for mid band gain?
A: Mid band gain values vary widely depending on the amplifier design, from single digits to thousands or more in multi-stage amplifiers.

Q4: How does feedback affect amplifier stability?
A: Proper feedback can improve stability and reduce distortion, but excessive feedback can cause oscillation and instability.

Q5: When is this calculation most important?
A: This calculation is crucial when designing audio amplifiers, RF circuits, and any application where both gain and frequency response need to be precisely controlled.