What You'll Build and Test Skills and Concepts You'll Learn/Integrate

More Cowbell!: Audio Preamp with Tone and Volume Control Active Filters—Op-amps and ﬁlters ENGN/PHYS 207—Fall 2019

Figure 1: The hit band L.E.D. Zeppelin. Their smash hits can be played back through an audio amp with master volume, bass and treble control knobs. You’ll build actual circuit “guts” for the bass, treble, master volume control knobs today!

What You’ll Build and Test

1. Some Legit Audio gear: Active tone control circuit (amplify or de-amplify bass and treble independently); and master volume control.

Skills and Concepts You’ll Learn/Integrate

• Active ﬁlters with op-amps and RC networks (tone control)

• Possibly voltage dividers or other op-amp based designs (volume control)

1 1 Tone Control Circuit Overview

Today we will build the classic and illustrious sounding Baxandall tone-control circuit (invented by PJ Baxandall in 1952—people have been smart for a really long time). The tone control allows the user to turn the bass up or down by turning a knob. Ditto for the treble. Want more cowbell, turn the knob fully CW. Want to get of that cowbell, then turn the treble knob fully the other way. The bass and treble act as are independent control knobs. See section 4

As a bonus feature, we’ll add a master volume control knob. This is a familiar audio feature: turning the knob on a pot adjusts the overall audio volume.

Before we get jammin’, you should know a few fun facts about human auditory perception:

1. Adult humans typically perceive frequencies in the range of 10 Hz to about 6000 Hz. (Babies are thought to hear up to about 15000 Hz, but they can’t really oﬀer verbal conﬁrmation).

2. Bass frequencies are low pitch notes. Typically, we think of the bass as frequencies ≤ 200 Hz.

3. Treble frequencies are the high pitch notes. Think piccolos, high hats, falsetto voice (Jonas brothers?). Typically we consider treble frequencies as ≥ 1000 Hz.

4. The “mids” are anything in between. Thing guitars, normal pitch vocals, etc. In the music world, mids are usually deﬁned as frequencies between 200-1000 Hz.

2 Design Constraints

This section lists various constraints and related considerations for your build today:

1. All circuitry must ﬁt within a minimal space of a single breadboard. Wiring should be neat and kept to a minimum.

2. Your design may incorporate a maximum of two TL082 chips (each has 2 op-amps inside, so a total of 4 op-amps max in total).

3. Power will be supplied using dual power supply operation of ± 9 V (we’ll use two 9V batteries in series for portable operation).

2 3 Input Pre-amp

An input pre-amp (Figure 2) is a clever little piece of circuitry that allows virtually any audio source to be properly connected into the circuit, regardless of the source’s impedance. Recall: all real sources are a combination of an ideal voltage source plus some output impedance.

Figure 2: Preamp consisting of passive RC high-pass ﬁlter + op-amp buﬀer. Image credit: TI TL082 datasheet

The pre-amp section also contains a 1-stage high pass filter. What is the cutoff frequency? Compute it and write this number down! The purpose of the HPF is to remove any dc offset component in the audio input signal. This likely isn’t of any practical import if you plug a mobile device directly into the circuit. However, it may very well be the case that an audio optical link has an offset centered around 2.5 V, but it’s only ac content (time-varying wiggles-and-waggles) in the signal that encode the audio content that we wish to propagate further down the circuit.

Lastly, note the 1 µF capacitor hanging onto the output of the op-amp buffer. This is known as an ac-coupling. It blocks any dc signal (constant in time stuff that contains no audio content) from flowing into the rest of the circuit. It’s not a bad idea to replace the 1 µF capacitor with an even bigger value (e.g. 10 µF).

For now, build the pre-amp circuit by itself. Later, you will connect it to the input of the tone control circuit. Verify the pre-amp is working. Connect an audio source at the input (e.g. laptop) and view the input signal on the scope. Simultaneously, measure the output from the op-amp. How do the input and output signals compare? Is what you see on the oscilloscope what you’d expect for a buﬀer?

3 4 Tone Control Circuit (Baxandall)

4.1 Background

This tone-control circuit (Figure 3), invented by PJ Baxandall circa 1952 (!), is found in virtually every stereo receiver. It is called a tone-control circuit because, the user can control how much much the bass and treble are “boosted” (amplified) or “cut” (deamplified) by turning the respective knob. The bass and treble level can be controlled independently of one another. A boost means those the sound level at those frequencies are amplified (G(f) > 0 dB). A cut means the sound level at those frequencies are attenuated (G(f) < 0 dB). The term flat means that the sound is neither boosted, nor cut (G(f) = 0).

Figure 3: A: Baxandall Tone Control Circuit with labeled component values. Note: wires are only connected where nodes are visible (small black dots); the wires that cross over near the inverting terminal are NOT connected. Double-sided arrow indicates pot wiper position for boost and cut, respectively. B: Simplified abstraction of circuit shown in A, an inverting amplifier configuration.

4 4.2 Theoretical Considerations

Before venturing on, one helpful bit of information: remember this circuit is used for controlling audible frequencies. For humans, the audible frequency range is about 10 Hz (deep bass) to 10 kHz (high treble). Amazing that the human ear can perceive frequencies over 3 orders of magnitude!

On ﬁrst glance, the Baxandall tone control circuit can be (probably is) intimidating. Fear not, dear 207er! You have all the knowledge you need to build the circuit and analyze its performance, both experimentally and theoretically. Here are a few hints to get you started:

The main thing to note is that we can conceptually approach this circuit by casting it in a simpliﬁed form (see Figure 3B), and breaking it down into two distinct parts, a bass subcircuit and a treble subcircuit.

4.2.1 Bass Subcircuit

First, let’s handle the the bass:

1. In view of of Figure 3, the bass subcircuit consists of impedance elements ZiB and ZfB alone. These are equivalent impedances combining: C1, C2, R1, R2, R3, and αB (bass knob setting). Draw the op-amp with only the bass subcircuit elements connected.

2. In view of Figure 3, develop expressions for ZiB and ZfB in terms of C1, C2, R1, R2, R3, αB (bass knob setting), ω and angular frequency of the input signal (rad/s). 3. To gain some intuitive sense of the bass subcircuit, draw it for two limiting cases, the familiar ω = 0, and ω → ∞. 4. At high frequencies, what is the effect of the capacitors in parallel with the pot? 5. At low frequencies, what do the capacitors act like? Therefore, what is the effect of the pot in the circuit? 6. Somewhere in between the two limiting cases lies the cutoff frequency. Similar to a simple RC filter, we can argue that the cutoff frequency should occur when the impedance of the

capacitor is equal to the impedance of the pot: Z˜ = Z˜ = 1 Z˜ . Given this argument, C1 C1 2 R2 compute the expected cutoﬀ frequency for the bass (units of Hz).

4.2.2 Treble Subcircuit

Now time for the treble! Our analysis is similar:

1. In view of of Figure 3, the treble subcircuit consists of impedance elements ZiT and ZfT alone. These are equivalent impedances combining: C3, C4, R4, R5, and αT (treble knob setting). Draw the op-amp with only the treble subcircuit elements connected.

5 2. In view of Figure 3, develop expressions for ZiT and ZfT in terms of C3, C4, R4, R5, αT (treble knob setting), and angular frequency of the input signal ω (rad/s). 3. To gain some intuitive sense of the treble subcircuit, draw it for two limiting cases, the familiar ω = 0, and ω → ∞. 4. At low frequencies, what do the capacitors act like? Therefore, how much current flows through this part of the circuit at low frequencies? Moreover, explain why the treble circuit can’t transmit deep bass frequencies. 5. At high frequencies, what element can we replace the capacitor with?Therefore, what is the effect of the pot in parallel with the pot? 6. Somewhere in between the two limiting cases lies the cutoff frequency. Similar to a simple RC filter, we can argue that the cutoff frequency should occur when the impedance of the

capacitor is equal to the impedance of the pot: Z˜ = Z˜ = 1 Z˜ + Z˜ . Given this C3 C4 2 R4 R5 argument, compute the expected cutoﬀ frequency for the treble circuit (units of Hz).

4.2.3 The Full Circuit: Bass + Treble

Lastly, we must recognize in fact the bass and treble circuits aren’t truly independent. It turns out the full transfer for this circuit is given by: ! ! ! V˜ Z˜ Z˜ Z˜ + Z˜ out = H˜ (f) = − fB fT iB iT (1) V˜in Z˜iB Z˜iT Z˜fB + Z˜fT

Note the first two terms by themselves should look familiar (or, the will look familiar starting next week when we formally study inverting amplifiers!). The first term has to do with only the bass, the second term, with only the treble. The third term is a sort of “mixture” term. If the bass and treble are ideally independent of one another, what should be the approximate magnitude of the mixture term? To help you answer this question, and intuit the three terms above, you might ˜ think about the decibel gain G(f) = 20 log10 |H(f)|.

4.3 Build, Test-Drive, Measure Frequency Response

Build the Baxandall tone control circuit. Firstly, have fun and play with it. Carefully listen how the sound quality changes based on position of the control knobs. If all is working properly, you should hear a clear audible diﬀerence...hopefully very satisfying!

Also during your test drive, observe the audio input and output signals on the oscilloscope (e.g., see Figure 4). What do you hear in relation to what you view on the oscilloscope? How does the sound change as you turn the knobs? How does the output signal change as you turn the knobs? You should be able to piece together a direct relation between what you see and what you hear.

For data collection, we’re going to pool data as a class to fully characterize the 5 possible settings of the tone control listed below. Your instructor will assign you one of these ﬁve cases–be

6 Figure 4: Example audio input (yellow trace) and ﬁltered output (blue trace). Evidently, the treble (high frequency) is nearly fully cut, while the bass appears to be attenuated to a lesser degree (partial cut). Image courtesy of Laws Smith, Circuits alumni fall 2017. sure you know which one before you begin data collection! Also, we’re going for both magnitude and phase response as a function of frequency.

Take a suﬃcient number of measurements such that you can quantify device performance and compare to theory. Make sure you acquire suﬃcient data points to fully asses its performance over the full human audible frequency range (≈ 10 - 10000 Hz). Carefully enter these into a clearly labeled Excel data table and submit to the box folder. The instructor will combine the data sets into one ginormous table for later analysis.

The ﬁve bass and treble settings for measurement include:

1. full bass boost, full treble boost: αbass = 0, αtreble = 0

2. full bass boost, full treble cut: αbass = 0, αtreble = 1

3. full bass cut, full treble boost: αbass = 1, αtreble = 0

4. full bass cut, full treble cut: αbass = 1, αtreble = 1

5. ﬂat bass, ﬂat treble: αbass = 0.5, αtreble = 0.5

7 5 Master Volume Control

Every stereo ampliﬁer has a master volume control knob. There are many ways to implement just such a volume control. Make any variant you wish! The output of the tone control circuit will ultimately be connected to the input of the volume control circuit. The output of the volume control circuit will connect to a stereo ampliﬁer for music playback!

If you are in need of inspiration: Figure 5 shows the (hopefully) familiar volume control circuit. It’s a passive volume control with no amplifiers involved. Yet! Feel free to modify the design, if you wish. Build the master volume control on your breadboard and quickly verify it is working properly. For proper operation of the of this resistor network acting as volume control, you’ll need op-amp buffer at the output. This ensures the volume control can be connected to any output downstream (e.g. commercial audio amplifier, LM386 amplifier, etc.) without affecting the operation of the volume control itself. Use a TL082 to make your buffer.

Figure 5: The familiar volume control circuit (from Assignment 1). R1 = 4.7k, R2 = 100k pot, R3 = 15k.

8 6 What to Turn In

The ﬁrst three bullet points must not exceed 3 pages max. Appendix with theory can be as many pages as necessary, neatly organized and clearly legible (“easy to read”).

1. Circuit schematics. Can present separate ones for tone and volume control (feel free to copy and paste, as needed). Label all actual component values!

2. Make a beautiful figure(s) summarizing magnitude and phase response vs. frequency for the tone control circuit. This graphic should make it easy to compare theory vs. experiment for your particular control knob setting. (Remember you tested one out of five possible settings.) Write a paragraph describing the main findings. Quantify any claims you make regarding (dis)similarity between theory and experiment.

3. Photograph of your ﬁnal design in lab, annotated as appropriate to indicate various control knobs and/or other circuit components.

4. Proof-of-concept video and/or oscilloscope screen shot(s) that clearly show the input vs. output relationship for your circuit. Choose any setting you want, but regardless of which you chose, you must elucidate in writing (a few sentences) the relationship between input and output signals based on the position of your control knobs. For instance, if you turned up the bass to full, and maximally cut the treble, do you see only the long period (low frequency) waves at the output?

5. Theoretical treatment: Provide an appendix for full theoretical treatment to ﬁnd the transfer function for the tone control circuit, as a function of bass and treble pot positions. See section 4.2. Congratulations!! You’ve made it to the end. Hopefully a melodious penultimate lab in Cir- cuits fall 2019. The ﬁnal project awaits!