# Band-Pass Filter Fundamentals With Dual OWON HDS2xx Scopes

#### By Jeremy S. Cook

Freelance Tech Journalist / Technical Writer, Engineering Consultant

Jeremy Cook Consulting

February 06, 2023

Blog

# Band-Pass Filter

(Caption: Ground on bottom contacts, signal in top left contact, signal out top right contact / Image Credit: Giacomo Alessandroni, CC BY-SA 4.0 via Wikimedia Commons)

A band-pass filter is a resistor and capacitor setup that allows frequencies between a lower cutoff and an upper cutoff (i.e. frequency band) to pass. It also induces a phase shift, which can be seen in the resulting, but is otherwise out of the scope of this article. The configuration is diagrammed above and set up on a breadboard in the image below, and mates a low-pass filter stage with a high-pass stage.

The cutoff frequency formula for each section is defined as fc = 1/(2πRC). So as each stage’s resistor or capacitor value increases, fc decreases. The high-pass fc (i.e. it passes frequencies higher than the cutoff) will be lower than the low pass fc (passes frequencies lower than the cutoff), so a smaller R * C combination will therefore be used on the low-pass stage than the high-pass stage. Frequencies outside of the pass band are attenuated by 3dB or more, meaning there is ½ the power output or less versus the input, or .707 volts out (or less) for every volt in.

# Scope Setup

(Image Credit: Jeremy Cook)

Reading about this is one thing, but actually seeing values change in real-time is something else altogether. For my setup, I used a .047µF capacitor on both stages. Resistor values equalled 4.7kΩ on the input stage, giving a lower fc of 714 Hz. 219Ω was used on the output stage to produce an upper cutoff of roughly 16,000 Hz. Rearranging terms in the fc equation allows one to solve for frequency, capacitor, or resistor values as needed.

From here, I connected my HDS242 as the analysis machine, with channel 1 reading raw inputs and channel 2 filtered outputs. One channel was initially reading twice what it should, but after resetting the scope to factory settings (System > F3 > F3) I was quickly back in business.

# Scope Analysis

Looking at this setup on a scope, you can see that no matter what the frequency, you do get some attenuation in your output signal. Also, while “cutoff frequency” would imply a binary relationship, attenuation is very much an analog affair. While very little voltage passes at 10 Hz, closer to fc–say around 700 Hz–the signal is not so much cut off, but muted.

These concepts are quite basic for the experienced electrical engineer, but they illustrate just how helpful having access to multiple data channels can be, especially if you can tune your input in real-time. For those just learning electrical engineering and controls concepts, having access to an oscilloscope, multimeter, and (optionally) signal generator could be a game changer for your education.

Since they can be had for about the price of a textbook (maybe less these days), access to a multi-purpose device, such as those in the HDS2xx series by OWON, could be a real bargain.

# What Tools Do You Actually Need?

(Image Credit: Jeremy Cook)

Being able to use the HDS2102S as a signal generator, while monitoring the results on the HDS242 scope in real-time, is quite instructive to get a “feel” for how filtering circuitry works. At the same time, it’s a good reminder that while it’s nice to be able to generate signals with your scope, it’s not quite as good as having a dedicated signal generator. A single device would mean you have to switch around between different modes for visualization.

For me, the HDS2102S is extremely convenient. I can see if signals look correct in oscilloscope mode, check resistor values, analyze connections, and more at a moment’s notice. Over the months since my original OWON HDS2102S review, it’s become a go-to tool for me. That being said, when shopping for test equipment, consider what you need, and the price point. An all-in-one solution may be perfect, but other options may make more sense for you!

Jeremy Cook is a freelance tech journalist and engineering consultant with over 10 years of factory automation experience. An avid maker and experimenter, you can follow him on Twitter, or see his electromechanical exploits on the Jeremy Cook YouTube Channel!

Jeremy Cook is a freelance tech journalist and engineering consultant with over 10 years of factory automation experience. An avid maker and experimenter, you can follow him on Twitter, or see his electromechanical exploits on the Jeremy S. Cook YouTube Channel!