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Designing A Pocket
Equalizer For Headphone Listening

(A HeadWize Design Series Paper)

In
audiophile circles, equalizers are prescribed only as a last resort to
correct imbalances in recordings and room acoustics for loudspeaker
playback. The case for using equalizers with headphones is simply this:
headphones by their very nature change the tonal balance of music. The
acoustic shaping that results from sound interacting with a listener's
head and outer ears varies from person to person and is missing in
headphones, which play directly to the eardrums. Therefore, not only does
music in headphones have a different tonal balance than was intended, but
each listener hears a slightly different presentation. If the listening
system includes an headphone virtualizer (such as Dolby Headphone),
equalization may help restore the imaging if the headphones have a
different frequency response than what the virtualizer expects.

While equalizers for home stereos and studios are available in range of
prices and features, are there any options for portable users? Koss
Corporation makes an inexpensive, small 3-band equalizer (EQ-30 and EQ-50)
for headphones that runs off 2-AAA batteries, but it has received less
than favorable reviews (poor filter action and poor headphone drive). Some
portable stereos have built-in equalizers, which are mostly inferior
gimmicks. These products obviously are not designed with audiophile
concerns in mind. The best way to get a high quality portable equalizer in
these times of audiophile minimalism is to build one. This article is a
collection of opamp-based equalizer designs that are all suitable for
portable use (except for one vacuum tube circuit, included for the benefit
of glass audio fans). Appendix
1 describes a DIY project: building a mini tilt equalizer/amplifier
for headphones. Appendix
2 shows how to use OrCAD circuit simulation software to model and
customize equalizers.

EQUALIZATION AND HEADPHONES

In addition to correcting tonal imbalances in headphones and
recordings, equalizers can, to a certain extent, alter the perceived
spatial characteristics of headphones. Headphone acoustic simulators, such
as virtualizers, electronically process stereo and multi-channel signals
so that they image outside the listener's head - as though they were being
projected by real loudspeakers. When an acoustic simulator is not
available, equalization can mimic some aspects of normal hearing. For
example, Ron Cole and John Sunier at the Binaural Source recommend a
"biophonic" curve (shown above) as a guide to setting equalizers to
correct for ear canal resonance and other differences in the spectrum
between speaker listening and headphone listening. (See Taking Sound in
Another Direction for more information.) The curve suggests boosting
three center points and is the basis for this article's focus on 3-band
equalizers.

Another reason for equalizing headphone sound has to do with human
loudness perception. When listening at safe volume levels, headphone sound
may not be as satisfying because the perception of loudness is frequency
and volume dependent. As shown in the Fletcher-Munson curves above, human
hearing does not become "flat" until the SPLs are at the threshold of
pain. Since the curves change shape at different loudness levels, accurate
loudness compensation would have to be dynamically adjusted to avoid
overcompensation - an unlikely feature in a rack-mounted commercial
equalizer, let alone in a hand-built pocket EQ. Nevertheless, a small
treble and bass boost can improve the perceived frequency balance of low
volume headphone sound.

PASSIVE 2-BAND BAXANDALL

The passive circuit in figure 1 is a variation of the famous Baxandall
circuit. It features a smoothly increasing ±6 dB/octave slope of boost or
cut. The bass and treble filters have a shelving response, although the
"shelves" are outside the audible range with these component values. The
filter equations in figure 1a predict the threshold and shelving
frequencies. When the bass control is rotated for maximum boost, the wiper
shorts out the .033uf capacitor. R3 and C4 form a frequency dependent
voltage divider that determines the shelf frequency of the boost. When the
treble control is set for maximum boost, the wiper bypasses the 10K
resistor. C1 and R2 form a high pass filter.

In addition to simplicity, the circuit uses commonly available parts.
Even the 100K log taper pots, which are usually hard to find, are sold by
Radio Shack as part number 271-1732 (in a stacked configuration for
stereo). At the midway point, the pot will have about 10K on one side and
90K on the other. For the treble control, the side with 10K parallels R2.
For the bass control, the side with 10K parallels C4. Note that this
circuit could be divided for an individual bass or treble control (R5 may
then be omitted - it helps isolate the bass from the treble circuit when
the two are put together).

The passive Baxandall must see a low impedance source and drive a high
impedance load to avoid loading the network and affecting the response
curves. Low impedance sources include the output of a portable stereo or
preamp. It can drive a headphone amplifier or high impedance headphones
(possibly with a series resistor to increase the load impedance), but
typical low power portables may not be able to drive headphones to
adequate volume. Since passive networks are not amplifiers, the gain is
simulated by dropping the "flat" response 20dB below the input, for which
a portable stereo may not be able to compensate.

The active version of the 2-band Baxandall shown in figure 1b
incorporates the frequency shaping circuit into the feedback loop of the
opamp. The feedback network is almost identical to the passive Baxandall.
The pots are now linear taper, and the double capacitors in the bass and
treble sections have been simplified to one per section. The input stage
serves as both an impedance buffer and as a phase correcter, so that the
output of the EQ is in phase with the input. The equations for this
circuit are shown in figure 1c. Unlike the passive version, this equalizer
has true voltage gain: ±10 (±20dB).

ACTIVE 3-BAND BAXANDALL

A 2-band equalizer is limited in its ability to correct trouble spots
in headphones. The circuit in figure 2 is an active version of the
Baxandall with an adjustable resonant filter acting as a midrange control.
Again, the inverting buffer at the input ensures that the equalization
stage sees a low source impedance and that the output phase of the
equalizer is non-inverting. The total gain/cut for any band is ±20dB.

As with the 2-band version, the treble and bass filters are shelving
equalizers (figure 4) - although the "shelves" occur outside the audible
range with these component values. A better shelving characteristic can be
obtained by moving the shelving frequencies closer together. With small
modifications to the center frequencies, this circuit could generate a
broad facsimile of the biophonic curve. One important characteristic of
the biophonic curve is the "dip" at 7.5kHz to simulate the ear canal
resonance of normal hearing. If diffuse-field headphones are used, they
probably already have a response curve with the ear canal resonance
compensation, and then the EQ will help adjust it for the individual
listener.

The treble and mid bands then are the most critical. They must be
spaced far enough apart to simulate the response dip at 7.5kHz. Moving the
treble shelving frequency higher to 20kHz will help. Because the operating
range of the midrange resonant filter overlaps with those of the bass and
treble controls, no simple equations can describe how changes in component
values will exactly affect the response curves. Applying the equations for
the 2-band version to the 3-band, they appear to predict the bass and
treble crossover frequencies on the 3-band, but not the gain for the
treble control.

The midrange control parameters must be set by experimentation. These
following changes are designed to have minimal impact on the bass and
treble responses:

R4 affects the overall midrange gain/cut. Increasing R4 will reduce
gain and shift the midrange center frequency higher. Decreasing R4 will
raise the gain and set the center frequency lower.

Changing C4 and C5 will shift the midrange center frequency without
affecting the bass or treble. To shift the center frequency higher
(lower), decrease (increase) C4 and C5 in proportion such that C5 = 5C4.
The frequency shift is proportional to the shift in the value of C5:
f1/f = C51/C5 - where f1 and
C51 are the new values.

This design has the virtue of being a single IC project (with the quad
version of the opamp), uses easier-to-find linear-taper pots, and is free
of inductors. R1 and R2 are chosen for unity gain, but the circuit can
also function as a headphone amplifier, if the R2/R1 feedback ratio is
made greater than 1. For example, setting R1 to 10K ohms (and C1 to 10uF)
would give the equalizer a "flat" gain of 10. Then a volume control in
front of the inverter would be a good idea. In selecting the opamp, it
should have a very high slew rate for high bandwidth and be able to run
off standard battery voltages.

Most quality, FET-input opamps will work (such as the LF353 from
National Semiconductor) when run from two 9-volt batteries or even one 9V
battery configured as a virtually grounded dual supply (see figure 10
below). The Burr-Brown OPA132 or OPA134 is especially attractive, with a
20uV/sec slew rate, no phase inversion and a power supply as low as
±2.5VDC. For the active equalizers circuit shown in this article, the
recommended battery supply is ±9V. Smaller power supplies will likely
cause an equalizer to clip frequently because of the high gains involved.

BANDPASS EQUALIZERS

Although the Baxandall circuits are good for general purposes, there
are discriminating headphone connoisseurs who insist on doing the least
sonic harm when applying equalization. In particular, the shelving
characteristic of bass and treble bands can make recordings sound
bass-heavy or excessively noisy (noise is less of a problem when listening
to digital recordings). Parametric equalizers have a bandwidth control
(also called a Q control) for each band to further narrow the response of
a resonant filter. Since each band has a minimum of 3 adjustments (gain,
frequency and bandwidth), a 3-band parametric would have at least 9
controls and a barrel of parts and is impractical to house in a truly
pocket-sized enclosure.

The bandpass filters of an octave equalizer can be preset with a high
Q. A 3-band graphic equalizer with high Q bands is rare, because 3 bands
usually do not offer enough flexibility when the filter action is narrow.
However, there are situations where a 3-band graphic equalizer might be
adequate, such as when the EQ is application specific and the center
frequencies are known in advance. Again, the number of parts to build a
high Q 3-band equalizer is probably more than can fit into a small
enclosure (although there are "graphic EQs on a chip" that might work).

For the purposes of improving headphone listening, such complexity is
not mandatory. The effect of a resonant filter with standard 6 dB/octave
slopes (figure 5) is broad only at maximum gain. Thus, the action of the
filter can be confined by not setting the gain to extremes.

The Wien bridge equalizer in figure 6 uses dual resonant filters to
isolate the effect of the bass and treble controls to the center
frequencies. A voltage divider at the input sets the signal level into the
filter which is then varied by feeding back the bandpass response into the
differential input of the opamp. The per-band gain is ±9 dB. Each bandpass
consists of a pair of RC filters, so the slope of boost or cut is 6
dB/octave on either side. Even when the controls are set at maximum gain
or cut (figure 7), the filters have little or no effect on the low, middle
and high portions of the audio spectrum.

Going back to the active Baxandall, that circuit's midrange resonant
filter could be duplicated for the bass and treble bands to target the
audio spectrum more specifically. To avoid the problem of overlapping
bandpasses complicating the design of a single EQ stage, each band should
have its own EQ gain block. Unfortunately, this strategy increases the
number ICs (2 quad and 1 dual IC) but the whole circuit should still fit
into a pocket-sized enclosure (although the pocket may be a little bit on
the large side).

The 3-band resonant equalizer in figure 8 ensures that the EQ stages
see a low source impedance by buffering the input signal via a
non-inverting voltage follower. (To make this circuit an amplifier/EQ,
change the voltage follower to a non-inverting amplifier.) Each EQ stage
(figure 9) is configured with a low, mid or high center frequency and a
±10 dB boost/cut. The outputs from these EQs are then mixed back at unity
gain for an overall gain of 3. This mixing stage is another point where
gain can be added to the system. Since each EQ stage and the summing stage
are inverting, the equalizer output has the correct phase.

Each EQ stage is a combination of low frequency and high frequency
shelving filters. In fact, C1 and C2 can be alternately switched out to
restore the circuit's low or high frequency shelving characteristic. The
center frequency and gain of a resonant filter are set by overlapping the
responses of the low and high pass filters. To design the filter, first
calculate the C1/C2 ratio by solving equation 1 (figure 9) for a given
maximum voltage gain (say 3 or about 10dB). Solve for C1 as a proportion
of C2 and substitute this equivalent for C1 in equation 2. Then choose a
center frequency and solve for C2 in microfarads. The shown C values set
the center frequencies suggested by the biophonic curve. BEFORE BUILDING
WITH THESE C VALUES, check out the sound with an existing equalizer.

Note that equation 1 for calculating gain does not work if the design
attempts to attain the same level of gain as a single-sided shelving EQ.
For example, the maximum gain of this circuit configured as a shelving EQ
(by removing one of the capacitors) is approximately (R2 || R3)/(R1 || R2)
which comes to about 10 or 20dB. However, solving for C1/C2 by plugging "A
= 10" into equation 1 results in a negative ratio for C1/C2. These
equations limit the maximum gain to about 8 or 18dBs - which is plenty for
most applications.

TILT EQUALIZER

The equalizer circuits shown so far are of the traditional type: they
divide the audio spectrum into bands with a separate gain control for each
band. The audiophile community has decried the use of such EQs, because
they are difficult to set properly without introducing coloration into the
audio signal - especially in the midrange. In the early 1970s, Quad Ltd.
believed that the proper role of equalization was to fix subtle tonal
flaws in the audio system. They developed a "tilt" tone control, which
first appeared on their model 34 preamplifier. Unlike the Baxandall
controls, the tilt control "tilts" the frequency content of the audio
signal by simultaneously boosting the treble and cutting the bass
frequencies or vice-versa. The effect is subtle because the control has a
maximum boost/cut of 3dB.

Figure
10

The tilt EQ can be very beneficial for correcting tonal flaws in
headphone sound, such as excessive brightness or darkness, without being
too sonically obtrusive. The above schematic (figure 11) is from a
preamplifier design by Reg Williamson and Alan Watling. It is a tilt
control with a center frequency of 900Hz and a maximum boost/cut of 6dB.
The circuit produces a shelving characteristic on either side on the
center frequency (see the graph below). When the pot is in the center
position, the EQ's response is flat (the bypass switch takes the EQ filter
out of the audio path entirely). Turning the control to the left
(counter-clockwise) lightens the sound; to the right (clockwise) darkens
it. Note that at the extreme settings, the tilt EQ does result in a phase
inversion.

Figure
11

TUBE-BASED EQUALIZERS

Although vacuum tube EQs can hardly be "pocket-sized," they are prized
by tube audio aficionados and sound professionals especially. All of the
active EQs described so far use solid state opamps. Although not well
known, vacuum tube opamps such as the Philbricks were available back in
the Golden Age of tubes, when analog computers required their precision.
Designing an Opamp
Headphone Amplifier includes an introduction to building tube opamps
(theory and schematics). These devices will work very well with the
resonant filter EQ designs shown in figure 10. In some cases, however, it
may be necessary to scale the feedback resistors up or down to meet
circuit preferences.

Figure
12

The circuit in figure 9a is a biophonic EQ that contains a simple tube
opamp made of an input differential pair and a 12AT7 follower (the 33K
resistors and the pots form the feedback network). Frequency shaping is
accomplished with 3 triode-based resonant filters that vary the amp gain
(each band can be adjusted ±12dB). The center frequencies can be
approximated from equation 2 in figure 9 with these modifications: C1 = C2
and R1 = 10K. Only 6 tubes are needed: 5 12AX7 and 1 12AT7. The filament
voltages are either 6.3VAC at 4A or 12VAC at 2A (twist the filament wires
for lowest hum). The dual 150VDC supply should be able to supply 60mA and
does not need to be regulated. The THD is less than 0.001% at 1V RMS.

Appendix 1: Build a Pocket Tilt
Equalizer/Headphone Amplifier

Of all the circuits listed in the article, the tilt equalizer may be
the most acceptable to audiophiles in terms of the simple circuit topology
and the subtlety and effectiveness of its action. Tom Edney built a pocket version
of the tilt equalizer, which he modified to drive his low-impedance Grado
headphones. This section describes Edney's modifications to the tilt EQ
circuit and provides construction details.

Edney built the tilt EQ to compensate for the brightness in his Grado
SR-60 headphones. He writes:

A couple of months ago when I got a pair of Grado SR-60s (my first
headphones costing more than $30), I was immediately struck by how
bright they are. I'd heard that Grados were bright when I had been
shopping for headphones, but not being an audiophile, I didn't really
understand the significance of "brightness". I tried burning them in for
about 60 hrs, but they showed only slight improvement. The more I
listened to them, the more displeased I was. The bass was lacking, and
the treble was way to prominent for my taste. This was aggravated by the
fact that I listen at very low volume, and as the Fletcher-Munson
Loudness Curves diagram indicates, the loss of low frequencies is
affected more strongly than other portions of the audio spectrum at low
volumes.

So because of the combination of bright headphones, low volume, and
personal preference, I had very fatiguing headphones. I could only go
for about 30-60 minutes at a stretch before I had to stop using them. I
considered returning the headphones, but first I looked around on the
HeadWize site for an answer, and found it in the Tilt Equalizer.

Figure
A1

Figure A1 is the circuit that Edney used. It has a direct bypass, and
R3 is omitted. Because Edney's headphones are low impedance Grados, they
need more current drive than the OPA134 can output when the EQ's bass
response is boosted. Thus, the output of the EQ section is buffered with a
Burr-Brown BUF634 to provide high current drive for low impedance
headphones. The feedback capacitors were changed to 2200pF to move the
center frequency of the EQ up to about 2.3kHz. Edney based this change on
listening tests with his Windows Media Player equalizer. He says:

Before building the Tilt EQ, I tested the idea using Windows Media
Player with its 10-band equalizer. I played around a bit with the
sliders until I got the sound I wanted, and saw that they formed an
almost perfectly straight negative slope crossing at the 7th band from
the left. Bingo! I knew then that the Tilt EQ was what I needed.
Although I hadn't worked on a DIY electronics project since high school
(over 20 years), the circuit diagram looked simple enough that I decided
to give it a shot.

The [original] Tilt EQ circuit seems to underboost the bass (and
over-reduces treble) compared to my settings on the Windows Media Player
EQ. I wondered if that was because the Tilt EQ's pivot point is at 900
Hz, and the 7th band on the software EQ is about 2 KHz. I just tried
replacing the 5600pF caps (C3/C4) with 2200pF caps, which should put the
pivot point at around 2KHz. At first there didn't seem to be a huge
difference, but after a while I found I could dial in a satisfactory
sound with the 2200pF, where I couldn't with the 5600pF. Then I took the
CD I was listening to and put it into my computer to see how my Windows
Media Player EQ settings sounded. They were identical. Now the ratio of
bass to treble seems higher, which is what I was looking for.

Figure
A2

Edney increased the gain of the first stage to 1.5, so that the bypass
volume level would be the same as the flat EQ volume level, when connected
to his Casio PCDP. Normally, gain matching is not required as all the
stages of the original EQ have unity gain, and the output of the EQ should
be at the same level as the input. However, when he hooked the tilt EQ to
another source, the volume levels became unmatched again.

Figure A2 is an alternate circuit which functions as both an equalizer
and headphone amplifier. The bypass only switches out the EQ network, so
the volume level is the same regardless of the bypass setting (R3 is
required). The input stage has been configured for a gain of 2. The value
of the volume control should not be higher than 10K ohms (audio taper).
Otherwise, the pot's impedance could load the feedback network and change
the gain of the first stage. Since the EQ is powered by two 9V batteries
(see below), the gain of the first stage should be no higher than about 4
to avoid clipping when the EQ's tilt is at full bass or treble boost.

Figure
A3

Figure A3 is the power supply. The two 9V batteries in series connect
to an RC network to create a ±9V output with a virtual ground. A single 9V
battery will not provide enough headroom for the EQ's output at full bass
or treble tilt. (For more information about virtually-grounded supplies,
see Designing an
Opamp Headphone Amplifier.) Edney decoupled the power supply pins on
each of the ICs with a pair of 10uF electrolytic and 0.01uF ceramic disc
capacitors.

CONSTRUCTION

The tilt control pot is a dual, linear type. Low value capacitors, such
as the 2200pF, can be hard to find in the preferred audiophile film types.
Silver mica (or dipped mica) capacitors commonly have this value, but can
be expensive; however, many surplus electronic outlets sell them at very
reasonable prices (for example, All Electronics has dipped micas
for about $0.35 each). If film or silva mica types are not available or
are not affordable, NPO-type ceramic capacitors can be used. NPO ceramic
capacitors are more stable than other ceramic types.

The PACTEC enclosure holds two 9V batteries. The bypass toggle switch
is mounted on one side of the enclosure. The illuminated power switch
(with green LED) is mounted on the other side. The circuit board is a
protoboard from Radio Shack. Edney listed the steps that he followed to
build the equalizer:

I successfully breadboarded one channel without the BUF. Then
soldered it to the circuit board. Audio worked and so did the pot.

Then I breadboarded a BUF634 to the one channel with success (good
audio, pot worked). I did not solder the BUF to the circuit board at
that point.

I soldered the second channel to the circuit board, no BUF. That
channel worked, and then I checked it with a breadboarded BUF. It worked
fine.

I added both BUFs to the circuit board.

I built the whole thing with solid wire I'd had on hand, but while
trying to fit the EQ into the enclosure I broke off a number of wires. I
had to completely rewire the EQ with stranded wire to keep this from
happening. Obviously a mistake only a rookie would make.

The dual 50K pot was almost impossible to find, especially in the
small 16mm configuration. I finally found it at Main Electronics in
Vancouver, B.C. (part number 08-1755). Excellent, fast service. I
mounted it with the middle of the rotation at 9 o'clock, so that it
would work much like the picture of the Quad Ltd. Tilt EQ shown in the
article. Since my knob is round, I considered adding a cosmetic straight
line (instead of just the little arrow) to the knob to more intuitively
reflect the slope of the tilt. I may still do that.

My biggest problem was that my headphone jacks were *mono*, not
stereo. Because they were switched they had three leads, and I trusted
the guy at the electronics supply store, when he told me they were
stereo. I was getting no audio, apart from a clicking sound in the left
ear at the rate of about 2 per second. Anyway, I've got stereo jacks now
and verified that it's all functioning properly. The darn thing works!

The Results

Because Edney's EQ does not have a volume control, the audio source
must have its own volume control. He had no trouble using the headphone
output of his Casio PCDP, but the EQ generated hiss when connected to the
headphone jack of his receiver. He says:

There is no discernable loss in sound quality with the Tilt EQ. I
find that for most CDs I set the Tilt EQ to about 10 o'clock (9 o'clock
is flat/no change). This small change warms up the audio just enough to
lose the fatiguing brightness of the Grados.

Since I'm not using a headphone amp, I plug the EQ into the headphone
jack on my PCDP rather than the line-out so I can use the built-in
volume control of the PCDP. That is what I matched the volume to. I'm
very pleased with the results. I really like being able to dial in the
brightness in response to the music, the headphones, and the audio
source (PCDP, Walkman, portable radio).

I consider this EQ to be just barely pocket size. It is quite
portable and is perfectly suited to my desk at work, but for use in a
pocket, I would make at least two changes:

try to make it even smaller (using the quad version of the opamp,
eliminate the BUF634 if possible, and use smaller power and bypass
switches or eliminate the bypass altogether),

put both the input and the output jacks on the front next to the
knob. This would fit better in a pocket than having the input coming
in on the side of the unit the way I've done it.

Someday soon I hope to change the bypass so that it includes the
input stage, as the original article intended. The true bypass seemed at
the time to be the best way since it completely removed the EQ, but gain
mismatch is a real problem when I switch audio sources.

Appendix 2: Simulating a Tilt
Equalizer in OrCAD PSpice

Circuit simulation software can be invaluable in designing or
customizing equalizer circuits. With complex EQ networks, this process is,
at best, a hit-or-miss proposition for hobbyists who do not have audio
test equipment like a signal generator and oscilloscope, and is still not
easy for those who do. EQ networks can quickly become too complex to
describe with simple equations. In multi-band equalizers, the action of
each band can influence the responses of the other bands. Again, there may
be no simple equations to represent the overall response of a multi-band
equalizer. While not always accurate, predictions of the frequency
response from simulations can guide the design process.

This section discusses how to use OrCAD Lite circuit simulation
software to simulate the performance of the tilt equalizer. OrCAD Lite is
free and the CD can be ordered from Cadence
Systems. At the time of this writing, OrCAD Lite 9.2 is the latest
version. OrCAD Lite 9.1 can be downloaded from the Cadence website (a very
large download at over 20M) and should work as well. There are 4 programs
in OrCAD suite: Capture, Capture CIS, PSpice and Layout. The minimum
installation to run the amplifier simulations is Capture (the schematic
drawing program) and PSpice (the circuit simulation program).

Download Simulation
Files for Tilt Equalizer

Download OrCAD Burr-Brown
Simulation Libraries

After downloading tilteq_sim.zip and orcad_bb.zip, create a project
directory and unzip the contents of the tilteq_sim.zip archive into that
directory. Then extract the contents of the orcad_bb.zip archive into the
<install path>\OrcadLite\Capture\Library\PSpice directory. The files
burr_brn.olb and burr_brn.lib are libraries containing simulation models
for several popular Burr Brown opamps, including the OPA134 used in this
equalizer.

Note: The Burr-Brown libraries contain some very large models
(such as the BUF634) that will not run in OrCAD Lite.

The two basic types of simulation included are frequency response (AC
sweep) and time domain. The time domain analysis shows the shape of the
output waveform and can be used to determine the harmonic distortion of
the circuit's output or to visually inspect the waveform for anomalies
like clipping. They both run from the same schematic, but the input
sources are different. For the frequency response simulation, the audio
input is a VAC (AC voltage source). The time domain simulation requires a
VSIN (sine wave generator) input. Before running a simulation, make sure
that the correct AC source is connected to the amp's input on the
schematic.

The following instructions for using the simulation files are not a
complete tutorial for OrCAD. The OrCAD HELP files and online manuals
include tutorials for those who want to learn more about OrCAD.

Frequency Response (AC Sweep) Analysis

Run OrCAD Capture and open the project file "tilt_eq.opj".

In the Project Manager window, expand the "PSPICE
Resources|Simulation Profiles" folder. Right click on
"Schematic1-freq_resp" and select "Make Active."

In the Project Manager window, expand the "Design
Resources|.\tilt_eq.dsn|SCHEMATIC1" folder and double click on "PAGE1".

On the schematic, make sure that the input of the amp is connected
to the V3 AC voltage source. If it is connected to V4, drag the
connection to V3. By default, V3 is set to 0.5V.

To add the Burr-Brown library to the Capture: click the Place Part
toolbar button (). The
Place Part dialog appears. Click the Add Library button. Navigate to the
burr_brn.olb file and click Open. Make sure that the analog.olb and
source.olb libraries are also listed in the dialog. Click the Cancel
button to close the Place Part dialog.

From the menu, select PSpice|Edit Simulation Profile. The Simulation
Settings dialog appears. The settings should be as follows:

Analysis Type: AC Sweep/Noise
AC Sweep Type: Logarithmic
(Decade), Start Freq = 10, End Freq = 100K, Points/Decade = 100

To add the Burr-Brown library to PSpice: Click the "Libraries" tab.
Click the Browse button and navigate to the the burr_brn.lib file. Click
the Add To Design button. If the nom.lib file is not already listed in
the dialog list, add it now. Then close the Simulation Settings dialog.

To display the input and output frequency responses on a single
graph, voltage probes must be placed on the input and output points of
the schematic. The probes should already exist on the schematic. If not,
here's how to add them: Click the Voltage/Level Marker () on the
toolbar and place a marker at the junction of R3a, R4a and C3. Place
another marker just above RLoad.

OrCAD does not have a functional model of a potentiometer. R5a and
R5b represent a 50K-ohm pot. When R5a = R5b = 25K ohms, the pot's wiper
is at the center. To "rotate" the pot to a clockwise or
counter-clockwise position, make R5a << R5b or R5a >> R5b,
but in all cases, the sum of these resistors must total 50K. For
example, in the schematic shown above, the equalizer is set for a bass
tilt with R5a = 1K and R5b = 49K.

To run the frequency response simulation, click the Run PSpice
button on the toolbar (). When
the simulation finishes, the PSpice graphing window appears. The input
and output curves should be in different colors with a key at the bottom
of the graph.

The horizontal axis of the graph does not have adequate markings to
determine center frequency of the tilt by eye. To display the PSpice
cursor, select Trace|Cursor|Display from the PSpice menu. A vertical
cursor line appears on the graph, and the Probe Cursor window appears
over the graph. Drag the cursor to the point where the output curve
(shown here in green) intersects with the input curve (shown here in
red). Then, the exact coordinates of the intersection are shown in the
Probe Cursor window on the A1 line. The first number (2.3101K) is the
center frequency. The second number (500mV) is the corresponding voltage
for that frequency.

Time Domain (Transient) Analysis

On the Capture schematic, make sure that the input of the amp is
connected to the V2 sinewave source (the default values are: VAMPL=0.5,
Freq. = 1K, VOFF = 0). If it is connected to V3, drag the connection to
V2.

In the Project Manager window, expand the "PSPICE
Resources|Simulation Profiles" folder. Right click on
"Schematic1-transient" and select "Make Active"

From the menu, select PSpice|Edit Simulation Profile. The Simulation
Settings dialog appears. The settings should be as follows:

Analysis Type: Time Domain(Transient)
Transient Options: Run to
time = 10ms, Start saving data after = 0ms, Max. step size = 0.001ms

To display the input and output waveforms on a single graph, voltage
probes must be placed on the input and output points of the schematic.
If the probes are not already on the schematic, follow the procedure in
step 8 of the Frequency Response Analysis to add them.

To run the time domain simulation, click the Run PSpice button on
the toolbar (). When
the simulation finishes, the PSpice graphing window appears. The input
and output curves should be in different colors with a key at the bottom
of the graph.

To determine the harmonic distortion at 1KHz (the sine wave
frequency), harmonics in the output waveform must be separated out
through a Fourier Transform. In the PSpice window, press the FFT toolbar
button (). The
PSpice graph changes to show the harmonics for the input and output
waveforms. The input and output curves should be in different colors
with a key at the bottom of the graph.

The fundamental frequency at 1KHz will have the largest spike. The
other harmonics are too small to be seen at the default magnification.
In the PSpice window, press the Zoom Area toolbar button () and
drag a small rectangle in the lower left corner of the FFT graph. The
graph now displays a magnified view of the selected area. Continue
zooming in until the harmonic spikes at 2KHz, 3KHz, etc. are visible.

Harmonic spikes should exist for the output waveform only. The input
is an ideal sine wave generator and has no distortion. To calculate
total harmonic distortion, add up the spike values (voltages) at
frequencies above 1KHz and divide by the voltage at 1KHz (the
fundamental).

Additional Simulation Tips

To change the value of any component on a schematic in the Capture
program, double-click on the value and enter a new value at the prompt.

Note: Simulations only approximate the performance of a circuit.
The actual performance may vary considerably from the simulation as
determined by a number of factors, including the accuracy of the component
models, and layout and construction techniques.

References:

Berlin, Howard, Design of Operational Amplifier Circuits
(1984).

Berglund, Rickard, "Ultra-Low-Distortion Graphic EQ,"
Glass Audio, 6/96, p. 40.

Burr-Brown Applications Notes (OPA132,
OPA134).

Graf, Rudolph Encyclopedia of Electronic Circuits,
Vols 1-6 (1985-1996).

Horowitz, P. and Hill, W. The Art of
Electronics (1989).

Jung, W. Audio IC OpAmp
Applications (1988).

Meiksen, Z. H. Complete Guide to
Active Filter Design, Opamps, and Passive Components
(1990).

National Semiconductor Application Notes (LF353,
LM349).

National Semiconductor Audio/Radio Handbook
(1986).

Texas Instruments Application Notes
(TLE2426).

Williamson, Reg and Watling, Alan, "A New Control
Preamp," Audio Amateur, 4/91, p. 10.

For the
latest updates, see the Project
Addendum.

c. 1998, 2000, 2001, 2002 Chu
Moy.
Questions or comments? Visit
the HeadWize Discussion
Forums.

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© Chu Moy, 2001