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), ! 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 ! = 0, and ! ! 1. 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 ! (rad/s). 3. To gain some intuitive sense of the treble subcircuit, draw it for two limiting cases, the familiar ! = 0, and ! ! 1. 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!).