The formula to calculate the Magnitude Response of Low-Pass Filter is:
\[ M_{Lp} = \frac{\text{modulus}(K)}{\sqrt{1 + \left(\frac{f_t}{f_{hp}}\right)^2}} \]
Magnitude Response of Low-Pass Filter refers to its ability to pass low-frequency signals while attenuating higher frequencies, showcasing high transmission for lower frequencies. DC Gain refers to the ratio of output to input in a system or device, often used in the context of electronics or signal processing. Total pole frequency refers to the maximum frequency at which a system can stably operate, determined by the combined effect of all poles in the system's transfer function. Pole Frequency High Pass is the point at which the signal has been attenuated by 3dB (in a bandpass filter).
Let's assume the following values:
Using the formula:
\[ M_{Lp} = \frac{\text{modulus}(0.49)}{\sqrt{1 + \left(\frac{90}{3.32}\right)^2}} = 0.018063269574378 \]
| DC Gain (K) | Total Pole Frequency (ft) | Pole Frequency High Pass (fhp) | Magnitude Response of Low-Pass Filter (MLp) |
|---|---|---|---|
| 0.4 | 90 Hz | 3.32 Hz | 0.014745526183 |
| 0.45 | 90 Hz | 3.32 Hz | 0.016588716956 |
| 0.5 | 90 Hz | 3.32 Hz | 0.018431907729 |
| 0.55 | 90 Hz | 3.32 Hz | 0.020275098502 |