# Professor Bode and the Modern Oscilloscope

Blog Post created by JohnnieHancock on Mar 22, 2017

When I was an electrical engineering student back in the 1970’s at the University of South Florida — go bulls! — two of my favorite classes were Control Systems and Analog Circuit Fundamentals. One reason I loved these classes so much was because we got to create Bode plots. I know, that sounds weird. I really enjoyed finding the theoretical poles and zeros and drawing Bode plots on my green engineering graph paper by hand (pencil, paper, and a ruler). Thank you Professor Bode; you are my hero! But when it came time to go into the lab to verify the frequency response of something like a passive or active filter design that we were assigned to build and test, there were no frequency response analyzers (sometimes called network analyzers) to be found.

In those days network analyzers were highly specialized and expensive multi-box systems from test and measurement vendors, including Hewlett-Packard (Keysight’s predecessor). Without

access to one of these expensive instruments in my EE lab, the testing process consisted of taking multiple VIN, VOUT, and Δt measurements on an oscilloscope while changing the input sine wave frequency on a function generator. After making 15 or 20 measurements, I would have enough measured data points to convert to gain (20LogVOUT/VIN) and phase shift (Δt/T x 360) using my trusty slide rule. I would then plot the results back onto that green engineering graph paper alongside the theoretical plots for comparison.

The days of plotting theoretical results by hand are over. Most engineering students today use MATLAB® to do that. And certainly the days of taking multiple VIN and VOUT measurements in the lab using an oscilloscope and a function generator set at discreet frequencies must be over, right? After all, the test and measurement industry now offers a broad range of frequency response analyzers (FRA) and vector network analyzers (VNA) that create gain and phase plots automagically. But those days aren’t over! Most undergraduate EE teaching labs are not equipped with frequency response analyzers. Almost all EE students today use the same tedious method of testing a circuit’s frequency response that I used back in ancient times. Why is that?

FRAs and VNAs are still considered by many to be a specialized instrument — especially in the university environment. In addition, the price of these instruments start at around US \$5,000 and go up from there. This may not sound like much for someone in the high tech industry that depends on this type of instrument to get to their testing done quickly, but almost all universities have to operate on a tight budget. A typical student lab bench (consisting of an entry-level 2-channel oscilloscope, function generator, digital voltmeter (DVM), and power supply) can be purchased for about US \$2,000 today. To equip an entire student teaching lab with an FRA at an additional US \$5,000 per test station would blow most EE lab budgets out of the water.

But now the process of making multiple VIN and VOUT oscilloscope measurements to create Bode gain and phase plots are about to be over for many EE students – at least for students at universities that equip their labs with a new Keysight oscilloscope. Keysight just introduced a family of low-cost oscilloscopes with an optional built-in function generator (Figure 2). And the best part is that automatic frequency response analysis (Bode gain and phase plots) can be performed on these student oscilloscopes at no additional charge on models that come equipped with the built-in WaveGen function generator and frequency response analysis (EDUX1002G and DSOX1102G). All of this functionality (oscilloscope, function generator, and frequency response analysis) can be had for just over US \$600. Let’s take a look at a measurement example of characterizing a passive bandpass filter using this new oscilloscope.

Figure 3 shows the schematic of a simple RLC circuit that we will test. At lower frequencies, the 1-µF capacitor dominates the impedance (XC = 1/2πfC) of this circuit and blocks most of VIN from getting to VOUT. At higher frequencies, the 10-µH inductor (XL = 2πfL) blocks most of the input from getting to the output. But in the mid-band frequencies, the 50-Ω load resistor dominates such that most of VIN reaches VOUT (~0 dB). By definition, this is a bandpass filter. We will now test it with Keysight’s new oscilloscope with the built-in function generator and frequency response analysis capability.

We begin by connecting the output of the generator to VIN and also probe VIN and VOUT with channel 1 and channel 2 of the oscilloscope, respectively. Figure 4 shows the frequency response analysis setup menu, which displays a block diagram to assist us in making proper connections. This is also where we can define which of the oscilloscope’s input channels is probing VIN, which channel is probing VOUT, the minimum test frequency, maximum test frequency, and test amplitude. For this test, we will use all the default settings. When we select Run Analysis, the oscilloscope executes the one-time  test, sometimes called a "sweep."

Figure 5 shows the test results. The blue trace represents gain (in dB) with scale factors shown on the left side of the display, while the orange trace represents phase (in degrees) with scale factors shown on the right side of the display. A pair of markers is also available to measure gain and phase at any frequency. The oscilloscope even optimizes magnitude and phase scaling factors automatically. But you also have the ability to establish your own scale factors manually after completion of the test. This is probably the easiest-to-use frequency response analyzer on the market today. At least that’s my opinion. And it has to be the least-expensive FRA because it comes standard (US \$0) with the purchase of an EDUX1002G or DSOX1102G oscilloscope, which is only US \$200 more than the baseline 1000 X-Series model (US \$449). But performance is not sacrificed. Using a proprietary measurement algorithm, this instrument can achieve up to 80 dB of dynamic range based on a 0 dBm (224 mVrms) input.

Using this new Keysight oscilloscope capability has sure saved me a lot of time in my job. And I bet it will save EE students a lot of time as well so they can complete their lab assignments on time!

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