Category: Electrical Engineering

Modeling Low and High Pass Filter Frequency Response

Posted on by Paul Shultz in AC/DC Principles and Applications, Electrical Engineering, Excel, javascript, Products

There are several different tools available to model a filter’s frequency response. For the most part, filter response modeling is a very straight forward. We can develop a modeling equation base on the frequency response of a passive, RC low pass filter.

Passive First Order RC Low Pass Filter Circuit

The passive RC low pass filter is a simple voltage divider circuit where the impedance of the capacitor changes based on frequency. Using the resistor and capacitor impedances we can create the filter transfer function. From this transfer function we can create our own filter modeling equation.

The voltage divider equation is given by:

The transfer function, H, is simply VOUT divided by the VIN.

Having the transfer function equation simplified and expressed in frequency (ω), we can find the transfer function magnitude to plot the frequency response.

A filter’s cutoff frequency is defined as the frequency where the filter output is 3dB lower than the input. For the passive RC low pass filter this is defined as:

Substituting the cutoff frequency equation the transfer function magnitude response becomes:

Note that the transfer function magnitude is only an expression of frequency that forms a generic frequency response equation. Normally a filter frequency response is expressed in dB, which uses the log function. Using several log identities we are able to create a simple frequency response equation.

Calculating 20*log of the magnitude transforms our result into dB.

From the simple passive RC low pass filter we have created a single equation that calculates the filter frequency response in dB that only requires the filter cutoff frequency. To model a high pass filter, f and fc are flipped.

As an example, the filter response model below uses the above equation in JavaScript and plots the filter frequency response using chart.js based on your inputs.

Filter Response


Input Data
Cutoff Frequency(Hz)
Filter Type
Filter Order


Cable Attenuation Calculator

Posted on by Paul Shultz in Electrical Engineering

When transmitting data over a coax cable it is important to determine the amount of signal attenuation that occurs for data recovery purposes. Signal attenuation changes based on the cable construction, signal frequency, and cable length. Prior to ordering cable and measuring the attenuation a good first step is to approximate your application’s signal attenuation. Although cable datasheets provide a wealth of information, generally your application’s cable length and data frequency will not be listed.

This page helps to calculate a coax cable’s approximate attenuation for a selected signal frequency and cable length. The calculation uses a generic, cable attenuation approximation model that is built using data from the manufacturer’s cable datasheet. A JavaScript based cable attenuation calculator is provided that accepts vendor’s cable attenuation parameters as inputs and calculates the signal attenuation for a specified cable length.

Cable Attenuation Approximation Model

Cable attenuation for any coaxial cable can be approximated using the equation below where frequency (f) is in MHz. Once the coefficients a, b, and c are known, finding the cable attenuation for a selected frequency is easy by applying the formula below.

The coefficients a, b, and c are found by solving a set of linear equations using information found in the vendor’s datasheet. These equations are the different attenuation values (α1, α2, and α3 ) at different frequencies (f1, f2, and f3) for a common cable length. The cable datasheet usually provides these values but you can also measure these values in the lab.

Cramer’s Rule (method of determinates) is used to solve for coefficients a, b, and c using the linear equation frequency and attenuation values.

These coefficients create an attenuation based on frequency for the common cable length used in the linear equations. To calculate the cable attenuation for a different cable length first convert your answer to dB per unit length and then multiple by the application cable length.

Model Verification

To validate the above model we used Belden RG-174 catalog data. The vendor supplied data is for a 1000 feet of RG-174 coax cable at three different frequencies.

nFrequency (fn)Attenuation (αn) for 1000 Feet
11 MHz19dB
210MHz33dB
3100MHz84dB
RG-174 1000′ Frequency vs. Attenuation

Solving the linear equations yields the coefficient values of a = 12.871, b = 6.020, and c = 0.109 for 1000 feet of cable. Data from the Belden catalog shows that 100 feet of RG-174 has an attenuation of 5.8dB at 50MHz. Our model approximates the 100 feet, 50MHz attenuation at 6.09dB.

Cable Attenuation Calculator

In the form below, enter your cable parameters (Input Data: common cable length, and frequency vs. attenuation values) for three different frequencies/attenuations at a common cable length. Enter your application’s data frequency and cable length (Find For:) and then click Calculate to display the Solution: for coefficients, Δ determinate, and your attenuation value.

Input Data:
Common Cable Length (ft)
Frequency 1 (MHz) Attenuation 1 (dB)
Frequency 2 (MHz) Attenuation 2 (dB)
Frequency 3 (MHz) Attenuation 3 (dB)
Find For:
Frequency (MHz) Cable Length (ft)
Solution:
a
b
c
Δ
Attenuation (dB)

When using this model with calculated coefficients, don’t forget to convert the attenuation into unit length and then multiply by your cable length. For the validation model example the result using a, b, and c is 60.9dB / 1000′ × 100′ = 6.09dB.

Notes

Normally attenuation values are entered as negative values in dB. You can use either positive or negative numbers to calculate the cable attenuation. Also the length units are arbitrary. You can use feet, meters, km, etc. as long as the units are consistent. Finally frequency values are always entered in units of MHz.