Abstract - The availability of inexpensive PC sound cards that can simultaneously play and record stereo digital audio files permits a single PC to function as both a signal generator and as a dual-channel recording digital oscilloscope. When the input and output of a linear analog circuit are recorded, for example, free or inexpensive software permits display of the input and output waveforms and spectra, as well as calculation of the magnitude and phase of the transfer function. Thus, students can perform measurements and calculations on simple signal processing circuits with their own PCs. The result is expanded utility of hardware homework, which before, despite popularity among students, was severely limited in applications beyond DC circuits.

Hardware homework found its first application in analog circuits courses, where students measured, for example, the voltage output response of a simple RC differentiator circuit to a rectangular voltage pulse with a duration of two time constants [1]. With a time constant of 10 seconds, the response was slow enough that students could measure the output of the circuit by reading the voltage every few seconds with an inexpensive multimeter. To avoid shortening the time constant of the differentiator though shunting the output resistor with the relatively low effective resistance of the inexpensive multimeter, students measured the output voltage of the differentiator through a simple operational amplifier voltage follower that they built directly on the same circuit breadboard as the differentiator. Students measured responses of an inverting operational integrator with a long time constant in a similar way. In the second summer semester of 1994, 14 out of 17 students found the hardware homework to be helpful and 16 out of 17 felt that it should be continued [1].

In a first year introductory course in electrical engineering, students built a simple DC transistor amplifier and measured its voltage gain by measuring the output voltage (with an inexpensive multimeter) as the input voltage changed for different settings of a potentiometer in the input circuit. In a survey taken in the course at the end of the fall semester of 1997, 76 out of 86 students agreed, or strongly agreed, that the hardware homework assignments were worthwhile. Surveys in subsequent semesters in this course show similar student support for hardware homework.

In the first analog electronics course, students designed and built an RC-coupled transistor amplifier and then measured its voltage gain by using a PC (personal computer) with a sound card. The output of the sound card provided the input to the amplifier as the PC played a MIDI (Musical Instrument Digital Interface) file. Simultaneously, the sound card recorded the input to the amplifier and the output of the amplifier in separate stereo channels. A built-in stereo player with graphic displays for each channel permitted the students to measure the gain of the amplifier by comparing the relative amplitudes of the input and output signals. Comparison of the measured gain with the design value provided immediate notice to the student, without direct intervention of the teacher, of any significant disagreement that should be reduced or explained. Anecdotal comments from students indicated that they experienced an intensely interactive learning environment as they tried to understand and reduce or eliminate discrepancies. In the spring semester of 1994, 20 of 24 students in the class found hardware homework helpful and 19 out of 24 believed it should be continued in the course [1].

Hardware homework thus has gained favor among students (and faculty) in different courses over the years. Students learn self-evaluation of their work in the interactive learning environment as they compare expected and measured performance of the circuits. Nevertheless, the limitation to crude measurements on AC circuits produced frustration in both students and faculty. The problem was not with using the PC sound card and a built-in stereo audio editor as a dual channel recording digital oscilloscope. That part worked just fine. The problem was that early PC sound cards could not play and record digital signals simultaneously. These cards could play and record simultaneously only by playing a MIDI file (analog, with an on-board FM synthesizer) and recording two (stereo) digital channels. The main obstacle in this approach is the practical difficulty of generating standard input test signals (sine, square, pulse, waveforms) in MIDI format. The emergence of PCs with full duplex stereo sound cards, owned by an increasing number of students, removed this limitation.

To accommodate telephony and audio conferencing via the Web, sound cards in most desktop computers now include full-duplex capability. Such cards permit simultaneous digital playback and recording of stereo audio files. Thus, they make it possible to measure the performance of a circuit, such as an amplifier, by utilizing a desktop computer with a single sound card and stereo audio editing software to provide a test waveform to the circuit and, simultaneously, to record both the test signal and the response signal from the amplifier in separate channels. Temporal and spectral analysis then can be performed on the recorded files. A desktop computer with a full-duplex stereo sound card can therefore serve as an audio waveform generator, a two-channel digital oscilloscope and a spectrum analyzer. In effect, a desktop computer with a full-duplex sound card can function as a network analyzer at audio frequencies.

A handy tool for utilizing the AWE64 as both a waveform generator and as a dual channel digital oscilloscope (and spectrum analyzer) is the audio digital waveform editor, Cool Edit from Syntrillium Software Corporation [3]. Even the free demonstration version of Cool Edit can record, read, edit and save digital mono and stereo sound files in most popular digital audio formats at various sample rates. It also can generate sinusoidal, triangular, and square waveforms either fixed in frequency or swept between specified end frequencies at a specified rate. Cool Edit can generate sinusoids in phase quadrature (indeed, pairs of various waveforms with arbitrary phase differences) as well as white and pink noise. In addition, its built-in Fast Fourier Transform (FFT) capability permits various types of frequency analysis. Additional features of Cool Edit not utilized here include the capability for AM and FM modulation and for digital filtering.

In short, the demonstration version of Cool Edit makes it easy to utilize the AWE64 SoundBlaster card (street price less than U. S. $100 in early 1998) as both a signal generator and as a dual channel digital recording oscilloscope. It is necessary only to open one instance of Cool Edit to generate the desired signal and to open a second instance to record simultaneously the input to the test circuit and the corresponding output in separate stereo channels. As a simple example, we first generate a sinusoid swept from 20 to 20,000 Hz over a period of 10 seconds. Although it is not necessary to save a file in order to use it to drive a test circuit, this file has been saved as LINEAR.WAV so that it is available on the CD-ROM for viewing or playing. This particular file is recorded in mono at a sample rate of 44100 bits/sec with 16-bit resolution. As the file name suggests, the frequency sweep is linear. To demonstrate the capability of Cool Edit to save audio files in ASCII text format, the file LIN50MS.TXT contains the first 50 ms of the content of the file LINEAR.WAV saved as text. The file LIN50MS.TXT can be viewed as text with any text editor or browser, or viewed and played as audio by Cool Edit.

To illustrate some other capabilities of Cool Edit, consider several views of the sound file, LINEAR.WAV. The spectrograph view in Fig. 1 shows the linear sweep in frequency from 20 to 20,000 Hz.
 
 

Fig. 1. A spectrogram of the waveform in the file LINEAR.WAV. (Horizontal units: seconds. Vertical units: arbitrary.) (Click image for larger view.)

On a percentage basis, the linear sweep is fast enough to distort the waveform from a pure sinusoid at the lowest frequencies, as shown in Fig. 2.
 
 

Fig. 2 The first 50 ms of the waveform in the file LINEAR.WAV. (Horizontal units: seconds. Vertical units: arbitrary.) (Click image for larger view.)

Such distortion can be reduced either by extending the sweep duration over a longer time or, for a given duration, beginning the sweep at a higher frequency. The distortion merely alters the Fourier spectrum to a degree that proves unimportant for most purposes, however. At higher frequencies, the distortion produced by sweeping the frequency is negligible.

Figure 3 shows the degree to which the waveform in the file LINEAR.WAV remains constant in amplitude as the frequency is swept.
 
 

Fig. 3 The entire waveform in the file LINEAR.WAV. (Horizontal units: seconds. Vertical units: arbitrary.) (Click image for larger view.)

The built-in FFT capability of Cool Edit permits calculation of the Fourier spectrum of the file LINEAR.WAV. Cool Edit produces the Fourier spectrum by scanning the waveform with a narrow-band digital filter, whose width and window shape can be specified. Figure 4 shows the spectrum that results from scanning the waveform with a triangular FFT window 8192 bits wide.
 
 

Fig. 4. The Fourier spectrum of the waveform in the file LINEAR.WAV with a linear horizontal scale. (Horizontal units: Hz. Vertical units: dB.) (Click image for larger view.)

As expected, the spectrum is flat except at the high and low frequency extremes where windowing effects, and the rapidity of the sweep at low frequencies, result in drop-offs. Figure 5 shows the same data displayed with a logarithmic horizontal scale.
 
 

Fig. 5. The Fourier spectrum of the waveform in the file LINEAR.WAV with a logarithmic horizontal scale. (Horizontal units: Hz. Vertical units: dB.) (Click image for larger view.)

If the drop-offs at the extremes of the swept frequency waveform are troublesome, white noise is an alternative signal with which to measure frequency response. The file WHITE.WAV, generated by Cool Edit, is a mono, 16 bit, 44186 bps, white noise signal. The first 50 ms of this file are shown in Fig. 6.
 
 

Fig. 6. The first 50 ms of the waveform in the file WHITE.WAV. (Horizontal units: seconds. Vertical units: arbitrary.) (Click image for larger view.)

Figure 7 shows its Fourier spectrum to be essentially flat over the entire audio range.
 
 

Fig. 7. The Fourier spectrum of the waveform in the file WHITE.WAV. (Horizontal units: Hz. Vertical units: dB.) (Click image for larger view.)

Figure 8 shows a Cool Edit recording of both the input to the high-pass filter (provided by a separate simultaneous instance of Cool Edit) and of the corresponding output of the filter. The input signal appears in the upper trace and the output signal appears in the lower trace.
 
 

Fig. 8. A few cycles of the input (upper trace) and corresponding output (lower trace) of the RC high-pass circuit (R = 1,000 Ohms, C = 0.1 microfarads) driven by a sinusoid with frequency 1592 Hz, the characteristic frequency. (Horizontal units: seconds. Vertical units: arbitrary.) (Click image for larger view.)

This figure clearly shows a phase difference of 45 degrees between the input and output voltages of the filter. The figure also shows the ratio of the output and input amplitudes is approximately (0.5/0.7) = 0.7, consistent with the expected factor of 0.7071 mentioned earlier.

As a second example, consider a simple band-pass filter that consists of cascaded single-pole opamp low-pass and high-pass filters designed to share a common cut-off frequency calculated from component values (20% tolerance) to be 1061 Hz. The input and output impedances of this configuration, once again, have values that do not require a buffer amplifier to increase the Line Input impedance of the AWE64. To measure the frequency response of the band-pass filter, the swept-frequency file, LINEAR.WAV, was played to provide input. A recording of the output voltage from the band-pass filter, as well as of this input voltage, is shown in Fig. 9.
 
 

Fig. 9. The input (upper trace) and corresponding output (lower trace) of the opamp band-pass circuit driven by a sinusoid with frequency swept from 20 to 20,000 Hz. (Horizontal units: seconds. Vertical units: arbitrary.) (Click image for larger view.)

The peak in the output trace during the frequency sweep clearly shows band-pass behavior. More quantitative information is displayed in the Fourier spectrum shown in Fig. 10.
 
 

Fig. 10. The Fourier spectrum corresponding to the output of the opamp band-pass circuit driven by a sinusoid with frequency swept from 20 to 20,000 Hz. (Horizontal units: Hz. Vertical units: dB.) (Click image for larger view.)

Notice that the Fourier spectrum of the input (upper trace) is essentially flat between 160 Hz and 14,000 Hz. The output spectrum of the band-pass filter (lower trace) peaks near 1280 Hz, well within expected tolerance variations from 1061 Hz. Notice that between 160 Hz and 320 Hz, the slope of the spectrum is 6 dB per octave (equivalent to 20 dB per decade) as expected for a first order filter. Between 7241 Hz and 14,482 Hz, the slope is, as expected, -6 dB per octave. Notice, also, the appearance of some ac hum at 60 Hz.

An alternative approach to obtaining a spectral view of the output of the low-pass filter is to drive it with a white noise signal generated by one instance of Cool Edit and to record and Fourier analyze the output with another instance of Cool Edit. Figure 11 displays the results for waveforms 0.9 sec in duration.
 
 

Fig. 11. The Fourier spectrum corresponding to the output (lower trace) of the opamp band-pass circuit driven by white noise (upper trace). (Horizontal units: Hz. Vertical units: dB.) (Click image for larger view.)

Note that the output spectra (lower trace) displayed in Figs. 10 and 11, obtained differently, are quite similar. From the input spectrum (upper trace), note the slight decrease in amplitude at the upper and lower frequency extremes. Nevertheless, this spectrum indicates that the output of the AWE64 is flat over most of the audio spectrum.

Time-domain measurements can be useful directly, without spectral analysis, of course. As a third example, consider a simple opamp inverting integrator with R = 10,000 Ohms and C = 0.1 microfarads (in parallel with a 100,000 Ohm resistor) that is driven by a 1 kHz square wave. The results are shown in Fig. 12.
 
 

Fig. 12. The input (upper trace) and corresponding output (lower trace) of the opamp inverting integrator circuit driven by a 1 kHz square wave. (Horizontal units: seconds. Vertical units: arbitrary.) (Click image for larger view.)

Notice the expected triangular wave that results from integrating the square wave. The droop in the input square wave indicates the drop-off in low frequency response of the AWE64.

One possibility is to save *.wav files in ASCII text format and then use the PROBE portion of PSpice to analyze the files. Not only does PROBE offer reasonably sophisticated capability for data display, spectral analysis and distortion analysis, it comes with the evaluation version of PSpice and hence is free [4]. To analyze a sound file with PROBE, first use Cool Edit to save the sound file as an ASCII text file. If the audio file is a stereo file, the ASCII text file contains two columns of data, one for each channel. For example, Cool Edit saves the square wave input channel and the integrated square wave output channel from the file INTSQW.WAV in the ASCII text format evident in INTSQWCE.TXT. The input channel appears in the left column and the output channel in the right column.

Next, we use the VPWL_FILE voltage source built into PSpice to produce a separate PSpice voltage source for each channel recorded in the ASCII text audio file. The VPWL_FILE voltage source produces a voltage source with a waveform specified by time and voltage pairs listed in an ASCII text file. The data for each channel in the ASCII file saved by Cool Edit, however, must be split out into two separate files that can be read by the corresponding VPWL_FILE source in PSpice. The content of the VPWL_FILE file for the left (input) channel that results from the file INSQWCE.TXT is given in the file LEFT.TXT and that for the right (output) channel is given in RIGHT.TXT.

By selecting the option within PSpice to create a PROBE file during analysis and calculating the open-circuit voltage of these two sources, each channel in the original audio file becomes available for analysis within PROBE. A short MS Quick Basic program easily accomplishes the required rearrangement of the data into separate files. An executable file is included here as COOL2PWL.EXE. Choosing the transient analysis option, with PROBE, in PSpice gives the output shown in Fig. 13.
 
 

Fig. 13. PSpice/PROBE view of the input (green trace) and corresponding output (red trace) of the opamp inverting integrator circuit driven by a 1 kHz square wave. (Horizontal units: milliseconds. Vertical units: arbitrary.) (Click image for larger view.)

The waveforms in Fig. 13 are, of course, similar to those shown in Fig. 12. Figure 14 shows the Fourier spectra of the waveforms in Fig. 13.
 
 

Fig. 14. PSpice/PROBE view of the input (green trace) spectrum and corresponding output spectrum (red trace) of the opamp inverting integrator circuit driven by a 1 kHz square wave. (Horizontal units: kHz. Vertical units: millivolts.) (Click image for larger view.)

As expected, the harmonic amplitudes drop more quickly for the triangular wave output than for the square wave input. The harmonic peaks are broad because the waveform consists of only a few cycles.

The same basic approach of saving sound files in ASCII text format with Cool Edit permits use of any number of analytical software applications to analyze recorded sound files. Fig. 15, for example, shows the Fourier spectrum calculated by Matlab from the ASCII text file for the output of the opamp bandpass filter data displayed earlier by Cool Edit in Fig. 11.
 
 

Fig. 15. The Fourier spectra, calculated from an ASCII data file saved by Cool Edit and fed into Matlab, corresponding to the output (green trace) of the opamp band-pass circuit driven by white noise (red trace). (Click image for larger view.)

Although the scales in Figs. 11 and 15 are different, the general similarity of the spectra computed by two different software applications is apparent.

A Matlab M-file named AUDRD2.M allows Matlab to directly read in an audio file (either mono or stereo) that has been saved in "ASCII" format from Cool Edit. This Matlab file will compute and plot v(t), the spectrogram, and the Fourier spectrum magnitudes for MONO audio files. For stereo files, it will also compute and plot the magnitude and phase of the transfer function, H(f)=V_out(f) / V_in(f). From the data, Matlab easily computes the magnitude of the transfer function for the opamp bandpass filter, shown in Fig. 16, and the phase of the transfer function, shown in Fig. 17.
 
 

Fig. 16. The magnitude of the transfer function for the opamp bandpass filter, calculated by Matlab from white noise input and output data. (Click image for larger view.)
 
 

Fig. 17. The phase of the transfer function for the opamp bandpass filter, calculated by Matlab from white noise input and output data. (Click image for larger view.)

Apart from the high and low frequency extremes where the output is small, the calculated curves agree well with expected theoretical behavior.

The main disadvantage of using ASCII text files for exporting and importing sound files into various software applications is the relatively large size of the files. A stereo audio file in ASCII text format is about three times as large as the same file saved in WAV or PCM file format. (A stereo WAV or PCM file sampled with 16-bit accuracy at 44,100 samples per second produces a recorded file of about 175 kB/sec.) Because Cool Edit can save files in PCM format and applications such as Matlab can read files such files directly, analysis can be less cumbersome than the ASCII text approach outlined above. Matlab is, of course, more expensive than the evaluation version of PSpice, especially because memory constraints in the student edition of Matlab limit its use to audio files of only a second or so in duration.

In comparing the results from these three different approaches to obtaining the magnitude of the transfer function, students received immediate feedback about their work on a problem without direct intervention of the teacher. Moreover, as students became interested in reconciling the results from different approaches, they were drawn into an interactive learning environment in which they progressed in learning the important skill of assessing their own work [1]. Asking the students to describe the results of their comparisons in a document file not only made grading the assignments much easier, it encouraged them to learn through reflection on their work. Because students incorporated, as objects, the relevant files from both their measurements and their simulations into the same document file with their comparison, grading the assignment is straightforward. With PSpice simulations, the total file size is reduced by embedding only the schematic capture (*.SCH) files rather than output or PROBE files, which can be large. Clicking on the icon for the embedded schematic capture file in the open document (MS Word for Windows, in this case) file automatically opens the student's simulation schematic for simulation in PSpice, provided the appropriate version of PSpice is installed on the computer. In that case, the simulation files are stored as temporary files that disappear when the simulation is closed.

To see the results from one of the more successful student efforts on the final project, open the Microsoft Word file FINAL.DOC. For the 13 students who completed the final project, the scores ranged from 29 to 99, the average being 81 with a standard deviation of 21.

Such hardware homework activity involves the student in a variety of learning activities ranging from concrete to abstract and incorporates a number of specific features increasingly held to be useful in realizing successful learning environments [5], [6].

For subsequent work, see [7].

[2] The necessary drivers can be downloaded from http://www.creativehelp.com/files/download.asp.

[3] A demonstration version of Cool Edit, as well as licensing information, can be found at http://www.syntrillium.com/cooledit/index.html. The demonstration version of Cool Edit can be used and distributed freely.

[4] An evaluation version of PSpice, as well as licensing information, can be found at http://www.orcad.com/Product/Analog/eval.asp. The evaluation version of PSpice can be used and distributed freely.

[5] A. Collins, "Design Issues for Learning Environments," in S. Vosniaadou, E. De Corte, R. Glaser, and H. Mandl, (eds.), International Perspectives on the Design of Technology-Supported Learning Environments, Lawrence Erlbaum Associates, Mahwah, NJ, 1996, pp. 347-361.

[6] M. Hagler and W. Marcy, "Computer-aided Instruction," in John G. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering, 3, pp. 648-668, Wiley, New York, 1999.

[7] D. Mehrl and M. Hagler, "Active Learning using Inexpensive Sound Cards for Circuits and Communications Experiments," Proc. 1998 Frontiers in Education Conference, CD-ROM file /papers/1251.pdf. Also, http://fie.engrng.pitt.edu/fie98/papers/1251.pdf.

David Mehrl
Texas Instruments
P.O. Box 869305 M/S 8479
Plano, TX 75086
USA
Phone: 972-575-4861
E-mail: d-mehrl1@ti.com

David Mehrl (S'82-M'90) is Associate Professor of Electrical Engineering at Texas Tech University. During a leave of absence from the University, he is working in the Digital Imaging group at Texas Instruments in Plano, Texas. He is a member of IEEE and the Optical Society of America.