Appendix A: Some Basic Circuit Theory

Voltage and Current Polarities and Conventions

Unless we are dealing specifically with the flow of electrons through a , we will assume current flows from positive to negative. This is called conventional current flow. Conventional current flow is used by virtually all manufacturers today on and IC data sheets, application notes, etc. As shown in Fig. A.1, drops across components will be designated using curved arrows. Think of these arrows as voltmeters that sense the voltage across a given component. The point of the arrow is equivalent to the positive lead of a voltmeter. Currents will be represented with arrow heads drawn on the wires in which the current is flowing. For the and the shown in Fig. A.1,if current is flowing the direction indicated, the current is positive, and the voltage dropped across the components will be positive.

Linear Circuits

Ideally, , capacitors, inductors, voltage sources, and current sources are elements. If you graph the current vs. voltage characteristic for a linear component you get a straight line, as shown for the resistor in Fig. A.1. One of the nice things about linear components is that we can use Ohm’s law (V ¼ IR) to relate I, V, and R. Because the plot of current vs. voltage is a straight line, we can pick any point on the line and get the same result for R ¼ V/I. , , and tubes are all nonlinear devices. An example is the graph of current vs. voltage for a typical diode shown in Fig. A.1. We can’t use Ohm’s law to characterize nonlinear devices because the quotient V/I is not a constant. Even though circuits that contain diodes, transistors, and tubes are nonlinear, in many cases we can treat them as if they are approximately linear and obtain useful analysis results.

D.J. Dailey, Electronics for Guitarists, DOI 10.1007/978-1-4614-4087-1, 385 # Springer Science+Business Media, LLC 2013 386 Appendix A: Some Basic Circuit Theory

Fig. A.1 Linear (resistor) and nonlinear (diode) devices

Series Circuits

A typical series circuit is shown in Fig. A.2. All circuit elements (resistors and a battery in this case) carry the same current in a series circuit. The various voltage drops across the circuit elements can be determined using Ohm’s law and Kirchhoff’s voltage law. Note that I have oriented the voltage-sensing arrows pointing counterclockwise on the resistors so that the voltage drops across the resistors will be positive. I did this because I like to work with positive numbers but the arrows could have been oriented the other direction, resulting in negative voltage values.

Kirchhoff’s Voltage Law

Kirchhoff’s voltage law (KVL) says that the algebraic sum of all around a closed loop is zero. The series circuit of Fig. A.2 forms a closed loop. If we assume there are no other resistors than those shown, we sum the voltage drops moving clockwise from the battery to obtain the KVL equation

0 ¼ Vin V1 V2 V3 Vn

Or, alternatively we could write Appendix A: Some Basic Circuit Theory 387

Fig. A.2 A series circuit

Fig A.3 A parallel circuit

Vin ¼ V1 þ V2 þ V3 þþVn

The general rule is that we add voltages whose sensing arrows are pointed in the direction we travel around the loop. We subtract voltages whose sensing arrows point against the direction we have chosen.

Parallel Circuits

A typical parallel circuit is shown in Fig. A.3. In a parallel circuit, all elements have the same voltage across them. The voltage drops across all elements in a parallel circuit are equal. That is,

V1 ¼ V2 ¼ V3 ¼¼Vn ¼ Vin

The current flowing through a given element may be determined using Ohm’s law, Kirchhoff’s current law, or a combination of the two. 388 Appendix A: Some Basic Circuit Theory

Fig. A.4 Example of a node with five branches

Nodes

A node is a point where two or more circuit elements are connected together. For example, in Fig. A.3, the entire top line of the schematic is a node—the top terminal of all of the resistors could be drawn connected at a single point or node. The circuit in Fig. A.3 has a total of two nodes. In Fig. A.2, each junction between resistors is a node, so this circuit has n + 1 nodes.

Branches

A branch is a path through which current can flow. The circuit in Fig. A.1 has one branch. That is, there is only one path through which current can flow. The circuit of Fig. A.2 has n + 1 branches, However, we could have started our numbering with IT renamed I1, in which case there would be n branches.

Kirchhoff’s Current Law

Kirchhoff’s current law (KCL) states that the algebraic sum of all currents entering and leaving a node is zero. A node with five branches extending from it is shown in Fig. A.4. You can arbitrarily choose the polarity of the current sensing arrows. For example, if we assume that arrows pointing to the node are positive, while those pointing out of the node are negative, the KCL equation for Fig. A.4 is

0 ¼ I1 I2 þ I3 þ I4 Ix

Referring back to Fig. A.3, application of KCL tells us

IT ¼ I1 þ I2 þ I3 þþIn Appendix A: Some Basic Circuit Theory 389

The Superposition Principle

The principle of superposition is used to analyze linear circuits that contain multiple voltage and/or current sources. The idea behind superposition is that we can determine the response for each source acting individually, then add these responses to get the complete response. For example, to analyze the circuit in 0 Fig. A.5, we can start by “killing” current source I1 and finding the output Vo caused by voltage source V1 acting alone. An ideal current source has infinite internal resistance, so when we kill a current source it is simply replaced with an open circuit. Redrawing the circuit with source I1 killed as shown in Fig. A.5,we 0 can find Vo using the voltage divider relationship.

0 R2 V o ¼ V1 R1 þ R2 2kO ¼ 12 V 1kO þ 2kO ¼ 6V

Next, we kill voltage source V1 and determine the output voltage caused by current source I1 acting alone. The internal resistance of an ideal voltage source is zero, so when we kill a voltage source we replace it with a short circuit. Redrawing the circuit with voltage source V1 killed we find R1||R2 ¼ 667 O, so the second component of the output voltage is 00 V o ¼ I1ðR1jjR2Þ ¼ 3 mA(1 kOjj2kOÞ ¼ð3mAÞð667 OÞ ¼ 2V

Fig. A.5 Example of the application of superposition in circuit analysis 390 Appendix A: Some Basic Circuit Theory

The net output voltage is the sum, or superposition of the two components.

0 00 Vo ¼ V o þ V o ¼ 6Vþ 2V ¼ 8V

Useful Formulas

Ohm’s law V V V ¼ IR I ¼ R ¼ R I V2 P ¼ IV P ¼ I2RP¼ R n series resistances

Req ¼ R1 þ R2 þþRn n parallel resistances 1 R ¼ eq 1 þ 1 þþ 1 R1 R2 Rn Frequency and period 1 1 2p o f ¼ T ¼ o ¼ 2pf ¼ f ¼ T f T 2p pffiffiffiffiffiffiffi Inductive and capacitive reactance j ¼ 1 1 j 1 1 X ¼ ff90 X ¼ X ¼ jjX ¼ C 2pfC C 2pfC C j2pfC C 2pfC  XL ¼ 2pfLff90 XL ¼ j2pfLjj XL ¼ 2pfL Bipolar transistor relationships

V VBE T V IC ¼ bIB IE ¼ IC þ IB re ¼ IC ffi ISe T ICQ Triode relationships m gm 3=2 gm ¼ mrP m ¼ rP ¼ IP ¼ kVðÞP þ mVG rP gm JFET relationships 2 2IDSS jjVGS gm0 ¼ ID ¼ IDSS 1 VP VP Appendix B: Selected Tube Characteristic Curves

Figures B.1, B.2, B.3, B.4, B.5, B.6, B.7, and B.8

D.J. Dailey, Electronics for Guitarists, DOI 10.1007/978-1-4614-4087-1, 391 # Springer Science+Business Media, LLC 2013 392 Appendix B: Selected Tube Characteristic Curves

Fig. B.1 12AT7 plate and transconductance curves Appendix B: Selected Tube Characteristic Curves 393

Fig. B.2 12AU7 plate and transconductance curves 394 Appendix B: Selected Tube Characteristic Curves

Fig. B.3 12AX7 plate and transconductance curves Appendix B: Selected Tube Characteristic Curves 395

Fig. B.4 6AN8 and triode plate curves 396 Appendix B: Selected Tube Characteristic Curves

Fig. B.5 6L6GC pentode and triode mode plate curves Appendix B: Selected Tube Characteristic Curves 397

Fig. B.6 6L6GC and EL34 triode mode transconductance curves 398 Appendix B: Selected Tube Characteristic Curves

Fig. B.7 EL34 pentode and triode mode plate curves Appendix B: Selected Tube Characteristic Curves 399

Fig. B.8 EL84 pentode mode plate and transconductance curves Appendix C: Basic Vacuum Tube Operating Principles

Diodes

The diode is the simplest vacuum tube. Recall that the vacuum tube diode operates by thermionic emission of electrons from a heated cathode within the evacuated glass envelope of the tube, as shown in Fig. C.1.

Reverse Bias

When the anode is at a negative potential with respect to the cathode VAK  0V, the diode is said to be reverse biased, and the current flow through the tube is approximately zero. This occurs because the free electrons around the cathode are repelled by the negative potential at the anode, as shown in Fig. C.1a.

Forward Bias

If the anode terminal is made positive with respect to the cathode VAK > 0V, electrons that are attracted from the cathode are free to travel through the vacuum to the anode, as shown in Fig. C.1b. This is condition is referred to as forward bias. The current that flows in a forward-biased vacuum tube diode is not a linear function of the applied voltage, but rather obeys what is called the Child–Langmuir law, which is

3=2 IA ¼ kVP (C.1)

The constant k is the perveance of the diode. A high value of perveance results in a diode that drops less voltage at a given forward current. For typical vacuum tube

D.J. Dailey, Electronics for Guitarists, DOI 10.1007/978-1-4614-4087-1, 401 # Springer Science+Business Media, LLC 2013 402 Appendix C: Basic Vacuum Tube Operating Principles

Fig. C.1 Vacuum tube diode operation

Fig. C.2 The addition of the grid creates a triode diodes, k ranges from approximately 0.003 to 0.00035. The forward bias current vs. voltage relationships for three common vacuum tube diodes, the 5AR4, 5U4-GB, and the 5Y3-GT, are shown in Fig. C.1c. All three diodes closely follow the Child–Langmuir law, with the value of k varying from 0.003 for the 5AR4 to 0.00035 for the 5Y3-GT.

Triodes

If we take a vacuum tube diode and place a fine wire control grid, in between the cathode and the anode (which we will now refer to as the plate), a triode is formed. A triode is shown in Fig. C.2. The function of the grid is to allow control of the flow of electrons from the cathode to the plate. Examine Fig. C.2a. In this case, there is no bias applied to the grid of the triode. That is, the grid and cathode are at the same potential, which in this case is ground, and VGK ¼ 0 V. Physically, the grid has very little cross-sectional area. This, plus the fact that the grid is at the same potential as the cathode means that nearly all of Appendix C: Basic Vacuum Tube Operating Principles 403

Fig. C.3 Plate characteristic curves for the 12AU7 the electrons that leave the cathode make it across to the plate. The grid leakage current is quite small, on the order of 1 nA or less, and so may be ignored in this discussion. With no bias, the plate current IP will increase with plate voltage VP just as it would for a normal vacuum tube diode. In Fig. C.2b, the grid is biased to a more negative potential than the cathode. Now, the positive potential of the plate exerts less attractive force on the electrons surrounding the cathode, and the plate current will be reduced relative to that which would flow with no bias on the grid. If we step the grid bias voltage from zero to some maximum value, a family of plate characteristic curves is generated. Figure C.3 shows the plate characteristic curves for the 12AU7 triode. The equation that describes these curves is

3=2 iP ¼ kðVP þ mvGÞ (C.2)

When there is no bias applied to the triode, the term m vG is zero, and (C.2) reduces to the standard Child–Langmuir equation for a diode (C.1).

Amplification Factor

The parameter m (Greek mu) is called the amplification factor. The value of m depends on the construction of the tube. For example the 6AS7-G is a low-mu triode with m ¼ 2, while the 12AX7 is a high-mu triode with m ¼ 100. The actual value of 404 Appendix C: Basic Vacuum Tube Operating Principles m varies somewhat from one tube to another of the same type, but it is generally close enough to the published value that in many cases we can consider it to be the same for every tube of the same type. This is in sharp contrast to bipolar transistors where, for example, beta may vary wildly from one device to another with the same part number.

Transconductance

The parameter that relates plate current IP to grid bias voltage VGK is called transconductance, which is designated as gm. We can plot plate current as a function of grid voltage at various plate voltage levels. This produces a family of transconductance curves, such as those shown for the 12AU7 in Fig. C.4. Transconductance allows us to view the triode as a voltage-controlled current source. Looking at the triode from an AC signal standpoint, we have

iP ¼ gmvG (C.3)

Where the AC plate current iP is controlled by the AC grid voltage vG. We are taking some liberties here, assuming that vG ¼ vGK, which is true when there is no cathode resistance in the AC equivalent circuit.

Fig. C.4 Transconductance curves for the 12AU7 Appendix C: Basic Vacuum Tube Operating Principles 405

Plate Resistance

The effective internal resistance of the plate rP is another basic tube parameter that is very important. For example, maximum power transfer from the tube to a load that is driven by the plate occurs when rP ¼ RL. Although it is generally not necessary to have a precise match between rP and RL, triodes with low plate resistance are better suited for driving low resistance loads than triodes with high plate resistance. Plate resistance, amplification factor, and transconductance are related by the following equation.

m ¼ gmrP (C.4)

Tetrodes

A tetrode is a four-terminal tube that is created with the addition of a screen grid between the plate and the control grid. The function of the screen grid is to shield the control grid from the plate, which reduces the effective input capaci- tance of the tube. The screen grid is typically held at a slightly less positive voltage than the plate and is often bypassed to ground to help keep the suppres- sor grid voltage steady and noise-free. The schematic symbol for a tetrode is shown in Fig. C.5.

Fig. C.5 Schematic symbol for a tetrode 406 Appendix C: Basic Vacuum Tube Operating Principles

The presence of the screen grid has some negative effects on tube characteristics as well. For example, since the screen grid is held at a relatively high positive potential, it will accelerate electrons as they move from the cathode toward the plate. The increased energy of the electrons striking the plate causes secondary electrons to be emitted from the plate back toward the screen grid. Many of these secondary electrons are captured by the screen grid, resulting in high screen grid current and power dissipation which is undesirable. The creation of secondary emission current can also cause undesirable nonlinear behavior of the tetrode, even causing under some conditions.

Pentodes

The undesirable characteristics of the tetrode are improved by the addition of a fifth element, called a suppressor grid. This forms a pentode. The schematic symbol for a pentode is shown in Fig. C.6. The suppressor grid is located between the screen grid and the plate inside the tube. Most often the suppressor grid is tied directly to the cathode, which holds it at a very negative potential relative to the plate. The function of the suppressor grid is to repel secondary emission electrons back to the plate, preventing them from causing excessive current flow and power dissipation in the screen grid. generally have much higher effective plate resistance rP, and amplifi- cation factor m, than triodes. The plate characteristic curves for pentodes are very similar to those of bipolar transistors and field effect transistors. The plate curves for the EL34 pentode are shown in Fig. C.7. Even though the pentode has a suppressor grid, the secondary emission electrons still affect the plate characteristics to some extent. Notice in Fig. C.7 how the low current plate curves dip or kink at low plate voltages. This effect is caused by

Fig. C.6 Schematic symbol for the pentode Appendix C: Basic Vacuum Tube Operating Principles 407

Fig. C.7 Plate characteristic curves for the EL34 pentode secondary emission, and it is even more pronounced in tetrode characteristic curves. For this reason tetrodes were rapidly superseded by pentodes. The pentode can also be configured to operate as a triode simply by connecting the screen grid directly to the plate. Operation as a triode significantly reduces rP, m, and maximum power output, but is often used to obtain particularly desirable overdrive and distortion characteristics. Index

A Baxandall tone control, 51–52, 162, 196, Absolute value function, 181, 221 276, 353 AC equivalent, 73, 77, 87, 90, 92, 104, 140, BBD. See Bucket-brigade device (BBD) 273, 274, 278, 280, 293, 303 Beam power pentode, 261, 262, 323 AC load line, 66, 274–276, 279–282, 285, 289, Beta independence, 74–75 293, 304, 308, 318–320, 325–328, 333, Bias, 4, 18–19, 61–66, 71–75, 90–92, 102, 112, 334, 339, 340, 343, 359, 361–364, 368, 114, 116, 118, 121, 125, 138, 147, 153, 370, 375, 380, 382 166, 169, 214, 222, 230, 235, 236, 259, Active region, 62–64, 72, 77, 90, 100, 101 264–266, 271, 296, 311, 317, 318, 326, Aliasing, 217, 218 327, 331, 336, 338 All-pass, 206–207, 209, 211, 212, 213, 218, Bias current, 112, 114, 118, 121, 123, 252 152, 169, 203, 228, All pass filter, 206–207, 209, 211, 212, 213, 311, 317, 326 218, 248, 252 Amplitude modulation, 121, 230, 236, 237 class A, 63, 64, 260, 356, 357, 358, 375 Anode, 18, 19, 189 class A1, 267 Anti-aliasing filter, 218 class AB, 64, 146, 171 Antiphase, 130, 295 class B, 64, 146 Asymptotic response, 8, 59 collector feedback, 132, 133, 135, 136 Attenuator, 25, 78, 79 voltage divide, 71–75, 102, 138 Audio frequency range, 60 Bipolar, 1, 14–17, 55, 61, 62, 68–71, 88, 89, 90, Audio taper, 40–43, 51, 97, 241, 245 94, 100, 106, 109, 112, 114, 127, 128, Automatic biasing, 264 130, 131, 149, 151, 154, 159, 165, 167, Auto-wah, 250–251 172, 188, 211, 224, 300 Bipolar power supply, 1, 14–17, 94, 106, 112, 128, 130, 131, 149, 154, 211 B BJT, 61, 62, 68–75, 89, 90, 94–106, 108, 126, b (beta), 62, 66, 67, 70, 74–75, 109, 133, 135, 133, 135, 136, 139–141, 151, 152, 154, 139, 152, 154, 155, 159, 187, 381 165–167, 181, 186–191, 193, 196, 198, Balanced modulator, 237–242 200, 201, 252, 268, 276, 282, 286, 293, Bandstop filter, 242, 243, 248 295, 311 Bandwidth, 57, 59–61, 84, 86, 110–112, 115, Bleeder resistor, 21 122, 138, 143, 243 Bode plot, 8 Barrier potential, 4, 16, 64, 70, 101, 119, 133, BP, 206, 243, 246, 247, 249–251 146, 147, 152–154, 159, 160, 169, 171, Bridge, 3, 4, 15, 16, 24, 35, 46, 181, 220 172, 180, 181, 199, 202, 221, 222 Bridge rectifier, 3, 4 Baxandall, 51, 53, 162, 196, 276, 353, 373 Bucket-brigade device (BBD), 213–218, 253

D.J. Dailey, Electronics for Guitarists, DOI 10.1007/978-1-4614-4087-1, 409 # Springer Science+Business Media, LLC 2013 410 Index

Bypass capacitor, 72, 73, 80, 84–86, 91, 94, (CE), 66–68, 71–86, 89, 94, 131, 267, 273, 293, 315, 366 99, 104, 116, 117, 134, 136, 139, 145, Bypassing, 80, 94, 102, 104, 153, 187, 200 191–192, 231 Common gate (CG), 68, 69 Common mode rejection, 29, 117 Common mode rejection ratio (CMRR), 108, C 117 Cadmium sulfide (CdS), 208, 209, 230 Common source (CS), 29, 68, 69, 88–91, 94, Capacitive coupling, 95, 267, 311, 312, 351, 99–105, 140, 187, 267, 273 378 Complementary-symmetry, 145 Cathode, 17–19, 189, 259, 260, 264–304, 307, Complex plane, 212 311, 315, 317–319, 322–324, 327, 328, Compliance, 78, 83, 148, 159, 209, 274–275, 331, 333–334, 336, 338, 343–345, 349, 280–282, 285–286, 289–290, 294–295, 350, 352, 356, 357, 360, 361, 366, 369, 299, 301, 308, 320–321, 328–329, 373, 383 334–335, 339, 375, 376 feedback, 264–267, 271, 322, 331 Composite transistor, 151–154 follower, 295–302, 360 Compound transistor, 151 resistor, 266, 271, 272, 297, 300, 318, 328, Compression, 226–231, 250 343–345, 352, 383 Compressor, 173, 226–228, 230, 236 stripping, 349, 350, 373 Conduction angle, 63 Cathodyne, 295–299, 301, 304, 305, Cord capacitance, 38

356, 360 Corner frequency (fC), 7, 8, 24, 38–39, 44, 45, CD, 226 48–50, 54, 59, 84, 85, 93, 125, 140, 141, CDA. See Current difference amplifier (CDA) 149, 218, 221, 243, 316 CdS. See Cadmium sulfide (CdS) Coupling capacitor, 72, 88, 89, 93, 95, 116, CG. See Common gate (CG) 128, 129, 145, 149, 185, 234, 235, 247 Charge pump, 130–132, 224, 239 Critical frequency, 206 Child-Langmuir law, 19, 24, 190 Crossover distortion, 146–148, 152, 155, 166, Chip, 9, 70, 100, 150–152, 214, 216, 238 171, 180, 181, 358, 359 Choke, 21, 22, 353, 373, 375, 378 Current difference amplifier (CDA), 121–124, Chorus, 218–220 143 Class A, 6, 61, 63, 65–68, 76, 88–91, 100, 102, Current gain, 56, 66, 67, 89 105, 113, 116, 132–136, 139, 140, 145, Current mirror, 118, 123, 147 153, 171, 181, 182, 186, 187, 192, 259, Cutoff, 61–63, 65, 145–147, 151, 226, 265, 260, 267–295, 307, 311–342, 351, 354, 269, 276 356–360, 375, 383 Class A1, 259, 260, 267 Class AB, 7, 61, 64, 67, 68, 145–148, 155, 156, D 171, 186–188, 312, 358 Daisy chain, 129–130, 132, 136 Class B, 6, 61, 63–64, 67, 68, 145, 146, 169, Darlington pair (Darlington transistor), 70, 180, 186, 187, 259, 312, 358, 359 151–153, 155, 156, 195 Clipper, 199–202 dBV (dBVrms), 126–127, 143, 144 Clipping, 63, 65, 82, 83, 88, 94, 104, 113, DC equivalent, 73, 267 134–136, 139, 140, 179, 181, 183, 187, DC load line, 133, 269, 270, 274, 277–280, 188, 191, 199, 200, 202, 214, 274, 275, 283, 285, 287, 289, 291, 293, 303, 304, 292, 295, 331, 347, 353, 366, 376 317–318 CMRR. See Common mode rejection ratio Decade, 8, 34, 54, 60 (CMRR) Decibel, 8, 56–57, 137, 226 Collector feedback, 132, 133, 135, 136 Decoupling capacitor, 13–14, 155, 164–165 Comb filter, 206, 207, 212, 213 Derating, 158, 172 Common base, 67–68, 116 Die, 150 Common cathode, 267–296, 298, 300, 303, Dielectric, 33, 36–37 304, 311, 360, 366 Differential amplifier, 117, 143, 235, 299–301 Index 411

Differential pair, 116, 117, 299–302 high pass (HP), 34, 37, 38, 49–50, 53, 54, Diode, 1, 3, 4, 8–10, 16–22, 63, 100, 147, 152, 84, 93, 140, 141, 149, 206 155, 160, 166, 169, 171, 172, 181, 190, IGMF, 243–247, 251, 254 199–204, 207, 221, 222, 228, 252, 261, low pass (LP), 7, 34, 38, 43, 47, 49, 50, 54, 349, 356, 366, 373 70, 125, 206, 218, 220, 221, 223, 224, Diode clipper, 199–202 230, 238, 316 Distortion, 23, 57, 58, 71, 78, 80, 82, 84–86, 88, notch, 209, 242–244, 249, 250 94, 96, 97, 99, 112, 113, 125–126, 135, response, 7, 8, 56, 126, 207, 212–213, 146–148, 152, 155, 163, 166, 171, 173, 243, 249 175, 178–181, 183–192, 196, 198–205, First-order filter, 7, 24, 37, 49, 50, 54, 84 214, 215, 238, 240, 276, 290, 298, 299, Fixed bias, 266 314, 324, 356, 358–360 Flanger, 211–218 Double-pole, single-throw (DPST), 1, 15, 115 Flanging, 211–213 DPDT, 191 Forward bias, 4, 15, 16, 18, 19, 70, 74, 75, 146, DPST. See Double-pole, single-throw (DPST) 153–154, 203, 222, 226, 230 Dropout voltage, 12 Frampton, P., 240 Dynamic emitter resistance (re), 77, 134 Frequency domain, 4–5, 7–8, 173, 176, 178, Dynamic plate resistance, 290–291, 316, 324, 186, 236 333, 345, 375 Full scale voltage, 226 Dynamic range, 226, 227, 253 Full wave rectifier, 3, 5, 16, 19–21, 24, 181, Dynamic resistance, 74, 203, 273, 315 221–223, 253 Fundamental frequency, 4, 5, 26, 27, 112, 176 E Fuzz, 96, 198–199 Efficiency, 18, 61, 63, 64, 145, 156, 187, 264, 309, 311, 358 Emitter bypass, 72, 73, 80, 84–86, 94, 104, 140 G Emitter follower, 67, 68, 116, 145–147, 152, Gain-bandwidth product (GBW), 108–110, 155, 171–172, 295 122, 142, 227 Envelope, 18, 23, 121, 220–228, 230, 232, 233, Gamma network, 316, 322–323, 331, 336, 236, 241–242, 250–251, 263 341–342 controlled filter, 250–251 GBW. See Gain-bandwidth product (GBW) follower, 220–226, 228, 230, 241, 242 Geometric mean, 245 Even function, 176, 177, 180, 182 Germanium diode, 199–200, 202 Exponential transfer characteristic, 188 Germanium transistor, 70, 71, 132–136 Global feedback, 87–88, 186 gm, 88, 91–93, 98, 99, 101, 103–104, 119, 120, F 140–143, 227, 253, 261, 262, 268, 276, Feedback, 85–88, 90, 109, 113, 114, 123–125, 282, 286, 293, 298, 305, 316, 322, 324, 132, 133, 135, 136, 165, 169, 172, 179, 330, 332, 336, 341, 352, 365, 372, 382, 186–188, 191, 202–204, 209, 211, 222, 384 228, 243, 264–267, 271, 322, 331, 336, gm0, 88, 89, 91, 92, 140 353, 375 Grid Feedback factor, 109 control (G1), 189, 290, 315, 316 FETs. See Field effect transistors (FETs) screen (G2), 290–293, 315, 323, 331, Field effect transistors (FETs), 55, 62, 68, 71, 336–337, 342, 375 98, 99, 105, 106, 165, 186–191, 227 suppressor (G3), 290, 292–293, 323, 324, Filter 343–344 all pass, 206–209, 211–213, 218–219, 248, Grid biasing, 266, 296, 318 252–253 Grid resistor (RG), 272, 278, 292, 293, 315, bandpass (BP), 206, 242–244, 322–323, 331, 336–337, 341–342, 345 246–251, 254 Ground loop, 163, 164, 378 bandstop, 242, 243, 248 Gyrator, 247–250, 255 412 Index

H 125, 128, 132–134, 138, 145, 146, 148, Half-wave rectifier, 221–223, 253 149, 152, 155, 156, 165, 167, 169, 170, Hard clipping, 188 187, 191, 194, 196, 223, 238, 263, 269, Harmonic, 5, 21, 27, 30, 36, 46, 80, 82, 112, 270, 272, 274–285, 287–289, 291, 293, 126, 127, 176–184, 187–188, 191, 192, 294, 295, 298, 299, 302–304, 307–313, 198–200, 202, 215, 218, 225, 238, 239, 315–320, 324–328, 333, 334, 338–340, 244, 356, 359 343, 345, 349, 352, 358, 359, 361–366, Harmonic distortion, 178–184, 188, 192, 215 368–370, 375, 379–384 Headroom, 12, 83, 132, 211 Load line Heat sink, 13, 145, 156–158, 167, 171 AC, 65–66, 274, 275, 279–282, 285, 289, High pass (HP), 34, 37, 38, 49–50, 53, 54, 84, 293, 304, 308, 318–320, 325–328, 333, 93, 140, 141, 149, 206 334, 339, 340, 343, 359, 361–365, 368, HP. See High pass (HP) 370, 375, 380, 382 Humbucker, 29–36, 43–46 DC, 133, 269, 270, 274, 277–280, 283, 285, 287, 289, 291, 293, 303, 304, 317–318 Local feedback, 87, 88 I Logarithmic amplifier, 202–205, 227 IDSS, 88–91, 99, 140, 141, 189, 252 Long-tailed pair, 116 IGBT, 151 Low dropout (LDO), 12 IGMF filter, 243–246, 251, 254 Low-frequency oscillator (LFO), 209–210, Impulse, 178 212, 213, 216–218, 231 Inductance, 32, 44, 54, 164–165, 243, 248, 249, Low pass (LP) filter, 7, 34, 38, 43, 47, 49, 50, 255, 311 54, 70, 125, 206, 218, 220, 221, 223, Inductive kick, 373 224, 230, 238, 316 Inductive reactance, 176, 249 Intermodulation distortion, 183–186, 191 Inverting Op Amp, 109–110, 114–115, 142 M Magnetic saturation, 310–311 Maximum power transfer, 307–308, J 311, 328, 381 JFETs. See Junction FETs (JFETs) Metal oxide FETs (MOSFETs), Junction FETs (JFETs), 68–69, 74, 88–101, 68–69, 90, 97–105, 119, 130, 135–136, 103–105, 108, 119, 135, 140, 141, 151, 141, 142, 151, 165–168, 181, 189, 190, 181, 189, 190, 193, 194, 196, 252, 264, 193, 196, 214, 252, 290 267, 273 Microphonics, 39 Midband, 59 Miller effect, 134 L Model, pickup, 34 Lamp, incandescent, 10–11, 208, 356 Modulation, 121, 220, 230, 236–240 Lamp, neon, 8–9, 11, 356 MOSFETs. See Metal oxide semiconductor Large signal bandwidth, 111 FETs (MOSFETs) LDO. See Low dropout (LDO) Motorboating, 163–164 LDR, 211, 216, 228–231, 246 mu (m), 57, 276, 282, 286, 290, 315, 352 Least significant bit (VLSB), 226 Multiple stage amplifier, 88, 94–97 LED. See Light emitting diode (LED) Lenz’s law, 25, 53 LFO. See Low-frequency oscillator (LFO) N Light emitting diode (LED), 8–11, 24, 200, National Electrical Manufacturers 202, 208, 211, 230, 251 Association (NEMA), 1 Linear taper, 40, 41, 50 Negative feedback, 85–88, 109, Loading, 3–6, 10–12, 14–16, 21, 22, 37, 39, 43, 114, 123, 165, 179, 187, 47, 53, 57–59, 63–66, 72, 77, 83, 84, 88, 188, 191, 266, 375 92, 94–96, 111, 113, 114, 116, 119, 122, NE-2 lamps, 8 Index 413

NEMA. See National Electrical Manufacturers response, 206, 207, 213 Association (NEMA) shifter, 53, 206–211, 213, 218, 248 New old-stock (NOS), 258, 276, 286, 297 shift oscillator, 124, 125, 209 Noninverting Op Amp, 113, 142, 249 Phaser, 209, 212, 213, 219 NOS. See New old-stock (NOS) Phase-splitter Notch filter, 209, 242–244, 249, 250 cathodyne, 295–301, 304–305, 356, 360 Noval base, 332 differential, 299–301, 305 Nyquist sampling theorem, 217, 253 transformer coupled, 301–302 Phasing dots, 308 Photocoupler, 208, 246 O Photoresistor, 208, 209, 228, 230, Octave, 8, 185, 239, 244 231, 251 Odd function, 176, 177, 180 Pickup Operational amplifiers (Op Amps), 7, 14, 55, humbucker, 29–36, 43–46 97–98, 105–117 phasing, 46–47 Operational transconductance amplifier piezoelectric, 35–39, 88, 91–94 (OTA), 118–121, 227–230, 253 single coil, 25–28, 30–35, 43, 44 Optocoupler, 208, 209, 216, 228, 230, 231 Piecewise continuous function, 179, 222 Orthogonal wiring, 379 pi filter, 21–22 Oscillator, 68, 79, 124–127, 130–131, 163, Pitch, 27, 174–175, 183, 185, 220, 230 209, 211, 213, 216, 218, 231, 236, Pitch shifting, 236–240 238–240, 259 Plate, 19, 189, 190, 259–260, 264, 265, OTA. See Operational transconductance 267–268, 272–276, 280–283, 286, 288, amplifier (OTA) 290–292, 295, 300, 303, 313, Output transformer, 165, 310–314, 316, 317, 315–316, 318–320, 322–326, 319, 321, 326, 329, 333, 335, 338, 345, 329–334, 339, 341, 344, 346, 349, 352, 357–359, 361–364, 369–370, 375, 380 353, 357–359, 362–366, 369–373, Overdrive, 63, 75, 82, 84, 97, 135, 173, 382–384 186–188, 192–199, 249, 290, 314, 324, curves, 269–271, 277, 278, 287, 293, 317, 342, 347, 353 328, 331, 332, 336–337, 345, 360, 368, 375, 376 resistor, 274, 296 P Pole piece, 26, 29, 30, 32 Parallel connected power transistors, 159–160 Potentiometer, 39–44, 47, 49, 52, 92, 96, 97, Parallel connected tubes, 307, 345–347, 383 166, 178, 194, 202, 209, 216, 218, 230, Parasitic oscillation, 115, 116, 155, 159, 163, 238–241, 245, 246, 248, 378 171, 314–315, 363 Power bandwidth, 111–112, 143 Passband, 7, 38, 243, 244 Power gain, 56, 57, 66, 67, 137 3PDT. See Three-pole, double-throw (3PDT) Power supply, 1–24, 61, 73, 94, 106, 107, 112, Pentode, 62, 257–262, 276, 290–295, 300, 308, 115, 122, 128–131, 148, 149, 153, 154, 315–317, 323, 324, 326, 327, 329–333, 157, 158, 164, 167, 170, 186, 211, 214, 336–344, 347, 348, 350–352, 355, 359, 224, 227, 264, 268, 276, 282, 287, 293, 366–373, 375, 376 307, 317, 326, 332, 347, 349–351, Period, 4–5, 24, 27, 36, 63, 165, 174–177, 220, 353–356, 366, 368, 373, 375, 378–380 230, 252, 349, 370, 373 Power transformer, 21, 128, 258, 264, 312, Periodic signal, 174, 177 313, 326 Permeability, 32 Preamplifier (preamp), 39, 68, 75, 84, 88, Perveance, 19, 20, 190 91–94, 112, 132, 192, 194 Phase, 29, 46, 47, 55, 57, 66, 67, 77, 80, 85, 89, Precision rectifier, 220–224, 241 96, 111, 130, 163, 173, 175, 177, 178, Push–pull, 145–150, 152–153, 155, 156, 183, 216, 219, 236, 240, 252, 254, 159–160, 165–169, 171, 180, 186–188, 295–302, 304, 305, 307, 353, 356–358, 259, 295, 298, 307, 308, 311–313, 350, 360, 363, 365, 366, 370, 371, 373, 384 356–363, 366–376, 383, 384 414 Index

Q Self bias, 90, 140, 264, 272, 278 Q-point, 63, 65, 66, 72–74, 76–77, 79, 80, 88, Sensitivity, 40, 78, 152, 156, 162, 216, 241, 91, 93, 94, 96, 102, 103, 133, 135, 138, 344, 347, 356, 366 139, 141, 186, 193, 200, 259, 266–272, Shelving response, 48 274–280, 282–289, 293, 294, 296, 297, Signal envelope, 220–221, 225, 227, 241, 251 303, 308, 318, 320–321, 325–329, 332, Single ended, 186–188, 300, 307, 311–342, 334–335, 338, 339, 343, 360–361, 363, 349, 354, 356, 360, 366 364, 366–370, 375, 382 Single ended amplifier, 187, 314–342 Quadratic, 99, 177, 183, 185, 186 Single-pole, single-throw (SPST), 1, 214 Quadratic formula, 103, 142 Single-pot tone control, 49–50, 160 Quality factor, 244 Sinusoidal waveform, 3, 23, 175, 178 Quiescent, 63, 72, 259, 276, 293, 303, 311, 317, Slew rate, 57, 60–61, 84, 111, 112, 115, 318, 326, 332, 349, 357, 360, 366, 375 120, 122, 138 Smoothing choke, 21 Snubber, 315–316, 363 R SOA. See Safe operating area (SOA) Radian, 175, 176 Soft clipping, 188 Rail splitter, 127–130, 132, 167–171 Source feedback bias, 90, 264, 267 RC filter, 24, 49, 50, 84 Source follower, 68, 69, 145, 165, 167 Reflected load resistance, 309–310, 312, 313, SPDT, 191, 214 316, 319, 324, 328, 332, 333, 338, 358, Spectrum, 5, 82, 126, 127, 173, 176–179, 359, 362, 369, 381–384 181, 182, 186, 200, 237, 238 Regulator, 6, 11–14, 17, 24, 56, 127, 164, 169 Spectrum analyzer, 82, 173 Relaxation oscillator, 209 SPST. See Single-pole, single-throw (SPST) Resistance coupling, 267–276, 302, 311 Square law, 99, 100, 189, 190 Resonance, 39, 249, 250 Star ground, 163, 164, 378 Resonant frequency, 254 Step function, 60 Reverb, 173, 232–236, 251, 307, 349–353, 355, Stop band, 7, 34, 38, 242, 243, 248 373, 374 Suppressor grid (G3), 290, 292–293, 323, 343 Reverb spring (tank), 233–235, 350–353 Sustain, 226–231, 250 Reverse bias, 4, 15, 16, 18–19, 90, 91, 100, Swamping resistor, 152, 159, 160, 345 146, 222 Switched-capacitor, 130 Rheostat, 42–43 Symmetry, 65, 106, 145, 149, 176–183, Ring modulator, 238–240, 254 187, 188, 199, 202, 220, 356, Ripple, 6, 7, 10, 11, 14, 17, 21–24, 358, 359 56, 156 Sziklai pair, 153, 155, 159 RMS. See Root-mean-squared (RMS) Rolloff rate, 34–335, 54 Root-mean-squared (RMS), 3–4, 23, 126–127, T

148, 156, 158, 261, 313, 322, 330, 335, T60, 233–235 340–341, 346, 365, 372 Talk box, 240–241 Tetrode, 62, 261, 323 Thermal resistance, 157, 158 S Thermal runaway, 159, 165 SAD. See Sampled analog delay (SAD) Three-halves law, 19 Safe operating area (SOA), 268, 269, 277, 368 Three-pole, double-throw (3PDT), 191 Sampled analog delay (SAD), 213–215 Time constant, 223, 232, 233 Saturation, 61, 62, 65, 88, 94, 148, 188, 225, Time domain, 173, 175–176, 178, 181, 185 226, 310–311, 357 TO-3, 70, 150, 157, 158 Schmitt trigger, 209 TO-220, 11, 70, 150 Screen grid (G2), 290–293, 315, 323, 331, Tone control, 23, 25–54, 96, 97, 160–162, 336–337, 342–344, 375 183, 195–197, 205, 276, 307, 347, Secondary emission, 292 351–353, 366, 367, 373 Index 415

Transconductance, 19, 20, 88, 91–93, 97–99, V

101, 103, 118–121, 140–142, VBE multiplier, 166–168, 172 190, 200, 203, 204, 227, 228, VCA. See Voltage controlled amplifier (VCA) 268, 271, 272, 276, 282, 284, Vibrato, 220, 230 286, 293, 316, 324, 325, 332, Virtual ground, 127, 128, 129, 169, 203, 222 345, 359, 381 Virtual short circuit, 114–115 Transconductance curves, 20, 98, 101, 190, Vocoder, 173, 240–242 200, 272, 284, 325 Voltage amplifier, 57, 99 Transducer, 25, 35, 94 Voltage controlled amplifier (VCA), 121, Transfer function, 41, 54, 56, 99, 177–183, 227–228, 231, 236–238 187, 188, 199, 200, 359 Voltage converter, 130 Transistor, 13, 22, 55, 61–75, 78, 80, 82, 88, 89, Voltage divider, 40, 41, 43, 54, 59, 71–75, 102, 90, 94, 99, 100, 105, 109, 111, 112, 112, 124, 127, 138, 231, 249, 250, 269, 115–119, 132–137, 145–148, 150–160, 299 163, 165–167, 169–172, 180, 182, 183, Voltage divider bias, 71–75, 102, 138 187, 188, 192–196, 198, 200, 226, 257, Voltage gain, 55, 57, 59, 66–68, 77, 78, 80, 82, 258, 260, 263, 267, 290, 300, 312, 345, 86, 89, 91, 93–96, 99, 102–104, 106, 351, 353, 356, 380, 381 111, 115, 117, 120, 123, 134, 135, 136, Tremolo, 211, 230–231, 236 139–141, 146, 147, 149, 153, 165, 171, Trigonometric identity, 185, 254 179, 182, 194, 195, 203, 249, 267, 268, Triode, 62, 188–190, 252, 257–262, 264, 265, 273, 275, 276, 279, 282, 286, 293–295, 268, 275–279, 282, 289–292, 294, 295, 298, 299, 301–305, 315, 321, 322, 329, 300, 315–317, 323–325, 329, 330, 332, 330, 335, 336, 341, 347, 352, 353, 365, 336, 342–344, 347, 348, 350–353, 366, 372, 373, 376, 379, 382–384 359–363, 366, 367, 375, 376 Voltage gain m (mu), 352 Trower, R., 220 Volume control, 25, 40, 41, 43, 92, 96, 347, 353 True bypass, 191–193, 231 Turns ratio, 308, 310, 321, 322, 329, 335, 340, 345, 346, 359, 363, 364, 370, 371, W 381–383 Wah-Wah, 53, 173, 242–250, 255 Wiper, 39, 42, 47, 49, 353

U Ultralinear (UL), 375–376 Z Underdamped, 34, 44 Zener diode, 166 Unilateral, 353 Zobel network, 165, 166