General Circuit Notes

Resistors
• Series R[total] = R1 + R2 +Rn
• Parallel R[total] = 1 / ( 1/R1 + 1/R2 + 1/Rn )
• Resistors can be paralleled to increase total wattage.
• "Johnson Noise" is the noise from the resistor as higher currents go through it. The higher the resistance value, the louder the noise. A higher wattage resistor will have less noise.
• Carbon resistors will color the peaks of audio with a type of pink noise. Use metal film for quieter operation.
• Wire wound resisters can handle a much higher wattage, but they often have a high inductance (unless they are specially wound). In some instances, the inductance can be an advantage (HF noise suppression).
• One can make custom wire wound resisters (both inductive and non) using a special high resistance wire and bobbin.
• Audio Quality Resistors: non-inductive wire wound, metal foil, high wattage metal film.

Capacitors
• Series C[total] = 1 / ( 1/C1 + 1/C2 + 1/Cn )
• Parallel C[total] = C1 + C2 + Cn
• New capacitors may need some burn in time to stabilize their operation (chemicals inside). This usually isn't more than a day.
• Smaller Farad sizes tend to sink higher frequencies better than larger.
• Tantalum (tantrum) capacitors are overly sensitive to reverse voltage and destroy easily. When destroyed, these often short out and can destroy other circuit pieces before and after it. Tantalum is good for low frequency power supply stability but is weak at medium to high frequencies.
• Electrolytic capacitors have frequency phasing problems and should not be used in the audio signal path.
• Ceramic capacitors are good for high frequency and how low inductance.
• Film capacitors are good for high frequency and have better linearity than ceramic.
• Audio Quality Capacitors (linearity): paper/oil, polypropylene, polystyrene, polycarbonate, polyester. Lower quality but tolerable: silver mica, ceramic (C0G/NP0 (more temp stable), XR7 (less temp stable than C0G)). Pysically bigger capacitors are usually cleaner and better. Film capacitors with separate film and foil are better than metalized film. Wima, Epcos, and Panasonic seems to be good brands.
• Black Gate capacitors use graphite instead of an electrolytic paste. They have a lower ESR and are non-polar. Most audiophiles prefer these for large capacitance sizes.
• All capacitors have a small amount of internal impedance (ESR). If 2 capacitors are paralleled, their resistance is less than that of a single capacitor (all other things being unequal). Often, 2 smaller capacitors in parallel can have less impedance and more Farads and the single capacitor equivalent. Sometimes a smaller and larger are paired up to make up for defficiencies in a single larger. Lower impedance means better damping in the circuit.
• All capacitors have a small amount of internal inductance (ESL). The amount is usually tiny enough to be ignored except for capacitor sizes over 1mF. A snubber (RC Zobel) can be used to help keep this under control.
• Cheaper capacitors have a slower slew charge time (30-40v/uS at best) and can limit the slew rates down the line.
• Smaller capacitors tend to charge up faster than a single large one.
• Ceramic capacitors usually have a low ESR. Aluminum electrolytic can get high. Tantalum is usually in the middle.
• A small and low ESL capacitor (ceramic 10-100nF) in parallel with a capacitance bank can help remove HF noise (ringing) caused by the higher ESL of the bigger capacitors.

Op-Amps
• Some op amps may need a warm up period to stabilize their sound. This usually isn't more than 15 minutes.
• Op amps (by nature) want to balance each input (make each the same voltage). The feedback gain resistors form a voltage divider and push the inverting input off forcing the op amp to balance differently. The result is higher output (gain).
• Op amps will have an output polarity based on the most positive input. If non-inverting is more positive, the output will be positive. If inverting is positive, the output will be negative.
• Some op amps have a minimum gain ratio and will be unstable with anything less. Op amps cannot have a gain less than unity.
• Overly high gain in an op amp will eventually cause some very high frequency to become fully back in phase (-360degrees). Instead of controlling that frequency, it will be repeatedly added to itself (a form of positive feedback) and cause the op amp to go into oscillation.
• Gain can be a funny thing in some op amps. Too high a gain ratio can increase the noise floor (use the gain ratio that is necessary for the application). High gain may limit how high the input signal can be before clipping. Some op amps are rated at 10% distortion (lousy) and to be clean need their gain to be cut by half or more. Some op amps use higher feedback (gain) levels to monitor the output and help keep output distortion lower by self correction (so higher=cleaner, up to a point).
• Open Loop Gain will have a flat frequency response at low frequencies then start to fall off shortly after (1kHz for better op amps). At the knee frequency, output impedance for above frequencies will increase as will distortion as the frequency is less able to feed back so the op amp can correct itself. The gain for higher frequencies will also be reduced as frequency increases. Faster op amps have this problem far less than slower ones.
• Long output cables have both capacitance and inductance and can act as an RF antenna. RF blocking on the op amp input will solve some problems, but the previous output is also connected to the cable and the noise may enter the audio path from there. A Zobel on the output will help prevent this backwards noise by acting as a low impedance terminator (but may not entirely solve it). This is not the fault of the cable. Any and all cables will behave this way. This is the fault of the sending and/or receiving amplifier(s). Better higher speed op amps tend to handle RF noise better than mediocre slower speed op amps.
• For best results, use a star topology for grounding. Voltages induced by ground loops can cause noise, distortion, and oscillation. Use large wires and wide traces for low resistance and inductance.
• In power op amps, return the speaker ground to power ground and not signal ground to increase stability and help prevent oscillation.
• Bipolar inputs require more input current than JFET's. Bipolar's often have a higher DC offset than JFET's (Ohm's Law).
• Higher impedance input op amps often have a clearer and crisper sound since less amps are being sucked out of the input signal to drive the amplifier.
• The feedback and ground resisters used to set the gain will develop a small voltage across them from the current due to Ohm's Law and can form an unwanted DC offset on the output. To balance this, another resister can be added to the other input line of the parallel value of the feedback and ground resisters.
• Sometimes a 1.5nF capacitor is wired directly on the input connector from signal to ground to block RF noise early on in the signal path.
• Sometimes a 50-500pF capacitor is placed directly between the input pins to remove RF noise.
• Zener diodes can be place on the signal input to help clamp down any signal that is too hot. The Zener voltage should be at least a few volts above the maximum expected voltage to reduce the chance of peak distortion.
• Diodes from the output to each power rail will protect against a heavily reactive load that might swing past the power rail voltages. This is typically only needed when the op amp is pushed hard into poorly designed speakers. This helps prevent over distortion and some op amps from being fried. The rail voltages "push" the diodes and keep them from conducting backwards on opposite output swings. When the output swings too high, the diode acts like a short and sinks the over voltage back into the power supply rails. Diodes often used: 1n4148, 1n4448, bat85, 1n400X.
• Use a low noise voltage regulator for the power inputs. PSRR of the op amp will reduce power line noise, but not by a large amount.
• The root-hertz voltage noise of an op amp plays a significant role in how quiet the overall circuit will be.
• A snub (RC Zobel) in the digital signal world is used as a high frequency sink and dampens the ringing on square waves.
• A snub (RC Zobel) in the audio world is typically used on the output of power amps to show high frequency resonance a low impedance path to ground. In reality these should also be used on signal level amps to avoid RF from becomming part of the audio signal. The main problem at signal levels is over loading the amp (which is only capable of mA outputs). Typically the resistor will be 100ohms and capacitor will be 1nF. This gives an Xc (capacitive reactance) of about 1mA (V=IR) at 20kHz. If the receiving end also has a Zobel, this could double. Try to stay below 100ohms since this is what the RF noise will see as a resistance. Try to keep the capacitor at or above 1nF so the trace capacitance doesn't influcence it. 100ohms + 1nF = 1.6MHz. Unfortunately to get the frequency down while still keeping in the 1mA range, 1k ohms is needed.
• Snubbers (RC Zobels) can be used on the power supply pins if large capacitors are desired.
• A snub (RC Zobel) on the output can be used to help stabilize the amp if an inductive load (speaker) is connected. Some sources say to use a resistor value equal to the speaker's resistance. These generally aren't needed for signal level op amps with short cables.
• Snubbers (RC Zobels) with resistor or capacitor values that are too large can actually induce instability instead of prevent it. A larger capacitor will sink more current (less Xc at lower frequencies) and heat up the resistor quite a bit. A resistor larger than 8ohm will block too much of the current that needs to be sunk for stability. Normal values are 1-8ohm and 47-100nF.
• Large capacitors on the op amp power pins will greatly help "tighten" and "clean up" the bass since the low frequency notes require the most energy to reproduce. A snub (RC Zobel) should be used if any power rail capacitor is >100uF. If there is only a single small capacitor and single large capacitor (>4mF), an additional middle value capacitor may be desirable.
• Parallel. This allows for more output current into a lower impedance load. Op amps wired for paralleled output will be able to drive a resistance of half of what they were originally rated for (good for 2ohm speakers). Any number of matched amps can be connected in parallel. Rindividual = Rload * Number_of_Ampifiers. Two amps connected to one speaker would each see that speaker as twice the impedance. Consequently, heat dissapation is less. Gain resistors are critical in this setup and should be matched to 0.1% tolerance.
• Bridge. Bridge mode output is a differential output method. Each amp will see half the resistive load (speaker). Op amps wired for bridged output will double their voltage swing. Theoretically 2 amps bridged together could be 4x more powerful than a single amp. Each individual amp doubles it power output and also doubles its heat output. The heat sink will have to be increased.
• Combinations of bridge+parallel output can be wired to increase overall power accordingly.
• Watch out for crossover distortion and thermal runaway if booster transisters are used on the output. Feed forward designs will also present a varying impedance on the output but generally have much lower crossover distortion. Extra stages in the feedback loop should be done with care. This can cause extra phase shifts that may lead to high frequency instability.
• Transistor boosters will need very clean power rails.
• Some op amps will need a resistor on the output line. At signal levels this can be used to help balance a differential cable or to prevent over loading the input of sensitive or older equipment. Signal level is usually 100-600ohm. Power level (0.1-10ohm, 1-10watt) protects the amp from capacitance induced oscillation (from poorly designed speakers). Small resistances are often used in paralled output to help balance the load between op amps. Be sure to choose a non-inductive resistor. The resistor can go inside the feedback loop, but will mess with the gain equation and will offer less protection (separation) fro the op amp's inputs.
• An inverting input op amp with a volume control in front of it could suffer gain problems if the impedance varies.
• Low pass filter in the feedback loop (from lm4780.pdf). This comprises of a capacitor+resistor in parallel with Rfb. The resistor is usually the same as Rfb. Equation (HPS7s can't solve this): (Rfb - Rgnd)/2 = Rfb || ( 1/(2*pi*Freq*Cfb) + Rfb2 )
• Power Supply Rejection Ratio (PSRR) and Common Mode Rejection Ratio (CMRR) drops dramatically with increased frequency. 100db at 100Hz may drop to 50db at 20kHz.
• Theoretical Power Dissapation for each op-amp in a chip: Watts = Vcc^2 / (2 * pi^2 * Rload)
• Some op amps have trouble with capacitive loading (as in long speaker cables). A 10ohm resistor in parallel with a 0.7uH inductor can stop capacitance induced ringing. This protects the amp from low impedances at high frequencies. The inductor provides low output impedance at low frequencies thus bypassing the resistor. The inductor blocks the high frequencies pushing them to the resistor thus providing capacitance decoupling on the output and reduce the Q of the series resonant circuit. 0.5-0.7uH can be achieved by wrapping 0.4mm enameled wire 10 times around a non-inductive resistor. People who argue a super-dollar speaker cable sounds so much better, often in reality, have an amplifier with output capacitance problems that the RL filter would fix.
• DSL op amps are designed for high frequencies (above audio range), low noise (has long telephone line runs), and low intermodulated distortion (255 closely spaced channels crammed into a limited range). These use current feedback (instead of the usual voltage) and have a very wide usable bandwidth (~10MHz). Current feed back amps typically have DC offset problems, lower input impedance, higher bias current, differential inputs don't have matched impedances, and gain setting is more difficult. Oscillation is a problem as if there is only a few pF to ground, it can become unstable. Models TI THS6012 (also THS1431?).
• Choosing Specs. Numbers don't always indicate good quality. Very low harmonic distortion (less than 0.1%, prefer 0.001%). Less than 25nV/rtHz of noise. Slew rates of 5v/sec or more. Wide unity gain bandwidth of 3MHz or greater. High open loop gain of 100db. High open loop bandwidth (bad ones only go up to around 100Hz, good ones go into the kHz range). Bipolar inputs with low open loop bandwidth can cause phase shifts and non-linearities with high level, high frequency input signals (FET inputs don't really have this problem). Unity gain stable op-amps are less likely to oscillate at high frequencies. Zero signal offset voltage should be 10mV or less. Low distortion (harmonic, IM, DIM, TIM).

Transistors
• General Purpose. 2n2218-2n2219 (npn 30-40v 0.6-0.8A), 2n3403 (?). pnp: 2n2904 - 2n2905 (40-60v 0.6A). 2n2222 (npn 40v 0.6A) + 2n2907 (60v 0.6A). 2n3904s (40v 0.1A) + 2n3906 (40v 0.2A)
  General Power. Some are also suited for audio. LM195 (?) npn. MJ4502 pnp (90v 30A).
  Matched Pairs Power (NPN+PNP). Some are also suited for audio. TIP35 + TIP36 (A=60v B=80v C=100v 25A), TIP41 + TIP42 (40v A=60v B=80v C=100v 6A), D45C11 + D44C11 (?). 2n3789 + 2n3791 (60v 10A). 2n3790 + 2n3792 (80v 10A). bd533-538 npn+pnp (33/34=45v 35/36=60v 37/38=80v 8A). BD911+BD912 (100v 15A).
  Signal Level Audio. BC546-550 npn + BC556-560 pnp (46/56=65v 47/50/57/60=45v 48/49/58/59=30v 100mA).
  Driver Audio: BD139 + BD140 (80v 1.5A). MJE340 + MJE350 (300v 0.5A). BC337-25 npn + BC327-25 pnp (45v 0.8A). BC338 npn + BC328 pnp (25v 0.8A).
  Power Audio (NPN+PNP): MJE/TIP3055 + MJE/TIP2955 (60v TIP=7A MJE=10A), MJ15015 + MJ15016 (120v 15A), MJ15003 + MJ15004 (140v 20A), 2sc3281 + 2sa1302 (nte2328 200v 15A), MJL3281a + MJL1302a (260v 15A), NTE2328 + NTE2329 (200v 15A), MJ21193 + MJ21194 (250v 16A, ON Semi, Power Base Tech, very rugged). Better MJL4281A + MJL4302A (350v 15A), MJE15034 + MJE15035 (350v 4A). General: 2n6121 (nte196) npn + 2n6124 (45v 4A nte197) pnp. 2n6122 + 2n6125 (60v 4A). 2n6123 + 2n6126 (80v 4A).
  JFETs: n-channel: 2N3819, J309, 2N5459 (25v 10mA).
• Transistor can vary in specs and quality quite a bit even from the same run.
• Transistors run coolest when fully off (no current) or fully on (no blocking resistance). The blocking resistance of the middle states causes varying amounts of heat.
• Transistor physics (amasci.com)
• Multiple transistors can be wired in parallel for lower noise. For every doubling, the noise figures change by -3db. Typically this is only practical with 2-6 transistors. Choose low noise transistors for better performance.
• BJT: to start opening up a collector-emitter, the base needs to be brought 0.6v above the emitter.
• BJT: NPN can be remembered by the arrow Not Pointing iNward. The arrow points in the direction of hole flow.
• BJT: The base is always the little "hat", the collector never has an arrow, and the emitter always has the arrow.
• BJT: Physically the base sits between the collector and emitter. The base is usually a few atoms thin and the voltage applied changes its resistance.
• BJT (old school diagram method): In a PNP, current will flow from the emitter (more positive) into the base (more negative) as the arrow symbol shows. In an NPN, current will flow from the base (more positive) into the emitter (more negative) as the arrow shows.
• BJT Manual Testing. These act similar to back to back diodes. Set the meter to resistance mode and put the meter probes on collector and base or emitter and base. A PNP transistor will have the red probes on collector or emitter and the black probe always on base. An NPN will have the red probe always on base and the black probes on collector or emitter. Red probe always goes to P terminal (positive) and black probe always goes to N terminal (negative). If the meter has a "diode check" function that shows the forward voltage drop of a diode, use it. The E-B junction will have a slightly higher voltage drop than C-B junction because the emitter is more heavily doped. This method can be used to check a transistor to see if it is good and identify an unknown type of transistor.
• BJT: beta ratio (also hfe) is how much CURRENT a transistor can amplify. It is expressed as I_collector/I_base. Beta tends to fluctuate some with the amount of collector current, temperature, and input signal frequency. Beta is usually highest with medium base currents applied.
• BJT Voltage gain from a transistor is dependent on beta, input impedance, and output impedance. The gain ratio is approximately: beta * (R_out / R_base). For db units: 20 * log (gain_ratio). If feedback is introduced, gain = R_fb / R_base. Beta is essentially removed from the equation if the gain is 10k or more.
• Higher gains can be achieved by cascading multiple transistor amplifiers together and using one feedback resistor from the last inverted output stage to the base of the first signal in stage.
• Equation: R <= (Vout*Beta)/Iout. Sets R to provide enough bias to transistor so it is saturated under Vout and Iout. R is connected from base to ground. Vout is tied to the collector. Emitter is tied to ground.
• Equation Gain: Common emitter voltage gain = beta * (Rout/Rin). Rout is the load resistor. Rin is the base resistor.
• N-MOSFETs take a positive charge on the gate-source. When the charge goes to 0 or negative, source to drain is fully blocked. P-MOSFETs take a negative charge on the gate-source.
• MOSFET symbols. N points inward, P points outward.
• Unsoldered MOSFET's are very static sensitive.
• JFETs are normally open and close with voltage to the gate. To close: Negative gate-source voltage for N-JFET, positive gate-source voltage for P-JFET. Drain and Source are interchangable terminals in many JFETs. JFETs use very low current on the gate (pico amps) compared to other transistors. This allows for lower noise amplifiers.
• JFETs may burn out if the gate-source voltage is reversed. N-JFETs gate must be <= 0, P-JFETs gate must be >= 0.
• JFET Gate-Source connection is a diode that can be checked with the diode function on a capable meter.
• JFET: Physically, the source and drain are the same piece of silicon and same doping. The gate is the opposite doping and wraps around that piece and the voltage applied (field) squeezes it close. The gate resistance is very high because the gate and channel form a diode. So long as the diode is reversed biased, resistance stays high. The jfet symbol arrow follows diode notation (positive pointing towards negative).
• JFET Symbols: N-channel points inward. P-channel points outward. If the source and drain cannot be interchanged, the gate is drawn offset towards the source lead.
• JFETs cannot handle high current and are usually used only at the signal level.
• BJT: Collector and emitter are not interchangable (like some other transistors). This is due to physical structure on the chip.
• BJT: The Base-Emitter junction are often called the diode of the transistor.
• BJT: Common Emitter Current Gain is represented as B[F] (Bf) or h[fe] (hfe) (beta). It is approximately the ratio of the DC collector current to the DC base current in forward-active mode and common-emitter configuration and is typically greater than 100. Common-Base Gain (alpha) should be approximately unity (99%). Alpha is calculated the same for all transistors: alpha = beta / (beta+1).
• BJT: If the load resistance is before the collector, the amp is a common emitter type (inverted output and has voltage gain). Common-emitter has the signal source and the load destination both connected to the emitter (sometimes connected through a battery or power supply). If the load is after the emitter, then the amp is the common collector type (non-inverting, beta+1 current gain, unity voltage gain).
• BJT: A common-collector amplifier is a buffer amplifier (voltage follower, emitter follower). Both signal source and load (ignoring power supplies) share the collector. The output voltage will be slightly lower than the input voltage for any beta value and load impedance. The output voltage will be about 0.7v less than input (forward bias voltage of the transistor). Cutoff occurs at input voltages below the forward bias and the power supply + forward bias. What increases is the current that can go with that voltage. The PNP version is a mirrored version of the NPN one. The output is still on the emitter line and a resistor/load is before that.
• BJT Darlington. The upper transistor in the darlington pair forms a common collector buffer which can drive a much larger current to the other transistor, which in turn, can drive a much larger total current. The overall current gain is (beta_1 + 1)*(beta_2 + 1). If the darlington is used in a common collector amplifier, voltage gain will still be unity minus the voltage drop of both transistors (0.7*2=1.4v). If even more current gain is needed, this can be expaned into a triplet or quadruplet configuration.
• BJT: A common-emitter amplifier is a voltage inverting amplifier. Transistors control current. As more current passes through the transistor, the voltage will drop.
• BJT: Small changes in the voltage applied across the base-emitter terminals causes the current that flows between the emitter and the collector to change significantly. This effect can be used to amplify the input voltage or current. BJTs can be thought of as voltage-controlled current sources, but are more simply characterized as current-controlled current sources, or current amplifiers, due to the low impedance at the base.
• In BJT linear circuit design, current control model is nearly linear (beta * base_current = collector current). The voltage control model requires exponents in the math.
• BJT: most are NPN because electrons are more mobile than holes (in PNPs).
• Negative feedback will increase bandwidth and decrease distortion.
• BJT: Negative feedback in a transistor can be done in 2 ways. (1) Collector to base resistor, since the collector output is inverted. (2) Emitter to ground resistor dropping voltage proportional to the emitter current through the transistor, having a negative influence on the base input signal through the base-emitter junction. The emitter's output is essentially a buffer. Vout is just a little under Vin on the base. If an emitter resistor drops more voltage at Vout, it has a reducing effect at Vin (R_feedback voltage drop + Vout = Vin). Keep in mind that this only makes sense if you understand that electrons actually flow backwards in a circuit (compared to conventional flow).
• BJT: negative feedback load in the common-collector amplifier circuit (by its very design name) prevents the transistor from thermal runaway (more current passing as it heats up). The feedback is a form a self correction and forms a very stable buffer.
• BJT: negative feedback in a common-emitter circuit will eliminate many of the quirks of the transistor through self correction, but gain is still dependent on beta (but now to a lesser extent). This can make one transistor look similar to a different one (within reason).
• BJT: Common-Emitter Negative Feedback trick to pass AC at maximum gain but control DC thermal runaway. To have the transistor control the DC component of the signal (this part leads to the thermal runaway, a hot transistor draws more bias current for the same amount of bias voltage, making it heat up even more) and not the AC, parallel the emitter-ground Rfb with a capacitor. AC will flow through the capacitor unimpeded but DC will be forced through the resistor and form a voltage drop lowering the DC gain. This method will mostly set the gain back to the beta value (which may or may not be desirable since beta fluctuates).
• PNP transistors are commonly operated with the collector at ground and the emitter connected to a positive voltage through an electric load. A small current entering the base prevents current from flowing between the collector and emitter.
• BJT: threshold, cut in, turn on voltage is usually 0.6v.
• BJT: The ratio of the collector current to the base current is called the DC current gain. This gain is usually quite large and is often 100 or more.
• BJT: It should also be noted that the emitter current is related to VBE exponentially. At room temperature, increasing VBE by about 60 mV increases the emitter current by a factor of 10. The base current is approximately proportional to the emitter current, so it varies the same way.
• BJT NPN: Base to ground turns off the transistor. Base to V+ turns it on. Set the base resistor to the mA needed according to Ohm's Law.
• BJT NPN Amplifier: The input AC signal is fed through a capacitor to remove DC and into the base. A forward bias resistor connects from V+ to base. To avoid distortion, set this to 0.6v + 1/2V. This will allow the signal to ride above the transistor turn on point and give the AC input signal maximum swing given a V+. The emitter is grounded. A load resistor is connected from V+ to the collector. This allows the output current to become a voltage (Ohm's law). The output point is between the collector and load resistor. Note that the output will have the DC bias on it and will be INVERTED. For non-inverted, the emitter-ground point is broken and emitter becomes output and the ground of the actual object (like a speaker) goes to ground.
• MOSFET: All are either N or P types. The gate is insulated and has no contact with the channel.
• MOSFET: N type: N source, P channel, N drain. P type: P source, N channel, P drain.
• MOSFET Symbols: N type arrow points inward to the middle of 3 pads and the wire connects to one of the pads. The P type arrow points outward.
• MOSFET: A positive voltage on P channel forms an N channel below the gate and conduction starts. A negative voltage is used for N channels.
• MOSFET: The input resistance is even higher than JFETs. The gate- channel resistance often comes close to 1G ohms.
• MOSFET: Since the gate is insulated by a thin layer of glass, pressure, over voltage, or static shock can easily destroy it.
• Operation Classes. Class A is always on and has a bias voltage half way between cutoff and saturation. This is the most power wasteful. Class B has the transistor on 50% of the AC waveform and is very efficient. An NPN+PNP in Class B "push-pull" configuration can accurately reproduce an AC waveform. Class AB is a hybrid and is on more than 50% of the time but less than 100%. This gives less distortion but at slightly higher power consumption than straight Class B. Class C has the transistor on less than 50% and is mainly used with fixed frequency L-C tank resonance circuits. Class D only has the transistor full on or full off at very high frequencies and is very efficient with little waste heat. The on-off pulses are averaged into an AC waveform and the harmonics are filtered out with a low pass filter. Class D is only practical for lower frequencies at high power (audio amplifiers and industrial DC to AC power inverters).
• When choosing a transistor: low noise (nV/rt-Hz), low resistance, high enough current rating, fast enough speed for the desired frequency (bandwidth), high enough gate/base and collector/emitter voltage (SOA Safe Operating Area), low enough turn on voltage, high linearity, high gain, temperature handling (hotter=less power, internal die temperature will always be higher). Power transistors: calculate with V=IR and determine maximum peak so it won't be blown.
• Higher quiescent current on the base generally leads to faster response times from the signal in to the output (better bandwidth). Power output transistors in amps will typically have 100-150mA quiescent current.

Diodes
• In a diode, the doping in the silicon has holes and electrons. The holes are attracted to the negative power source. The electrons are attracted to the positive power source. When a diode conducts forward, the power source pulls the holes and electrons together in the silicon and the 0.7v drop is required to push them over in normal fashion. When the diode is reversed, the holes are attracted to the negative power source and electrons to the positive, thus leaving a wide non-conductive gap where the P and N silicons meet.
• Shottkey Diodes (low loss): 1n5817, HP59082-2810, 1n5712, MBR330
• Regular Diodes: 1n400x (rectifier, 0.7v drop), 1n914
• Silicon diodes have a forward voltage drop of about 1.2v.
• Small Signal Diodes (~0.5v drop): 1n4148, 1n4448.
• Light Emitting Diodes (LEDs) can have a forward voltage drop of 1- 2.5v depending on the material.
• Multiple rectifier diodes back to back will increase the voltage drop across them in total.
• Multiple Zener diodes back to back increase the total zener voltage.
• Two Zener diodes pointing towards each other (or away) like on a signal input (AC waveform) will limit the total input peaks and clip anything higher.
• A regular diode pointing towards a zener will offer thermal stabilization (one goes up and the other down when temp changes).
• A bunch of LED+Zener diodes in parallel (with different and increasing zener voltages) can be used to form a simple voltage bar graph. Tapping off multiple regular diodes in a series can do the same thing (each has a 0.7v drop).
• Diodes + capacitors in a laddar formation can form a cascade multiplier for AC being converted to a higher DC.
• A diode bridge with 100nF capacitors wired in parallel with each diode slows down the diode switching and can remove much of the switching noise. Sometimes a resistor is wires in series with the capacitor.
• An LED hooked up to the base of an NPN transistor (pointing away and connected to negative terminal) can be used as a light sensor. An LED isn't as efficient as some others, but will work.

Power Supply
• Mains Wiring: put the fuse before the on/off switch to protect the line against hot shorting to neutral or ground. Use a DPST (not DPDT) switch to turn power on and off to prevent the other terminals from going hot when the switch is thrown and to protect against hot and neutral being wired backwards.
• Chasis grounding codes usually state the ground wire goes to a dedicated tab on the metal case that is non-supporting and has a lock washer.
• Clean ground return should use large wire and wide traces for low resistance and low inductance.
• Large capacitor banks with transformers and diode bridges. Ripple current from the capacitor bank recharging can be quite heavy pulses. Rate both the transformer and diode bridge for higher currents.
• Twisting together long supply and ground leads to an amp will help minimize inductance on the rail lines.
• Filtering RC. Very low ohm (0.5-2) resistors between capacitors form an RC filter and can help prevent line noise getting into and out of the load circuit. RCRCRC filter patterns are often used for greater filtering. Resistors are often cement type. Avoid inductive resistors.
• Inrush Current. RC filtering can help slow down the inrush a little bit, but not by a huge amount. A dedicated inrush blocking system should be used with 50-100mF of capacitors. Also when using a transformer of 300VA or larger.
• Power Switch. Putting 4.7nF Y-Rated caps across the switch terminals can help reduce popping (these caps fail safe).
• High Quality Ground? Signal ground is separated by these 4 stacked in parallel: diode pointing one way, diode pointing other way, 10ohm resistor, 100nF capacitor. Earth and Chasis are connected to the far side of this.
• AC Mains Interference Suppression. Yrated 2n2F to 47nF capacitors from hot to ground and neutral to ground.
• Signal ground can be isolated from power ground by a 10ohm resistor.
• Choose voltage and amp ratings with power surges in mind. Ideally incoming voltage is always clean and stable. In reality this is never the case.
• Rail Capacitors. Typicall 2-3mF of capacitance is needed per peak ampere of output.
• Initial Safety. When building a higher wattage amplifier (mainly transistor but also includes op-amp based), do not just plug it in to receive full power for the first time. If something isn't balanced quite right or is broken, it could blow out the expensive parts and potentially start a fire. For safety, use a type of variable limiting resistor on the main AC input line (an incandescent light bulb, 60-100watt range). As the filament in the bulb heats up, the resistance increases and less power is given to the amp. The amp will still run, but at much lower (and safer) volume levels. When the light goes bright, the amp is trying to pull a lot of current. A flash will happen naturally at power on as the capacitors load. If no signal is present, the light should go dim again. If the light latches on full bright, something is wrong and power needs to be removed (Class A power amps will probably keep the light on constantly, but probably not overly bright). If the light flashes on and off with no signal, the amp has stability problems.

Audio
• Filter. RC Filters can cause phase distortion and should be minimized.
• Filter. Linkwitz-Riley is a method of filter alignment between filters and not an alignment type itself. It is typically used with a pair of cascaded 2nd order Butterworth filters.
• Filter. Decade: A 10:1 (or 1:10) ratio of frequency. 100Hz to 1000Hz is one decade.
• Filter. Octave: A 2:1 (or 1:2) ratio of frequency. 440Hz to 880Hz is one octave (Musical "A" note).
• Filter. Quality Factor (Q factor). The inverse of the filter's damping. Higher Q gives more ripple for low and high pass filters. It also makes band pass/stop filters more frequency selective.
• Filter. Order: how fast the frequency rolls off. A first order drops 6db/octave. To get db rolloff, multiply the order number by 6.
• Filter. RC low pass filters must have a low impedance ground return to work.
• Filter. Generally with op amps, the resistor impedance shouldn't be lower than 1000 ohms or else the op amp may have trouble driving it.
• Filter. Cascading multiple filters should be limited as the following filters will present a load and actually shift the calculated frequency somewhat.
• Filter. It's generally better to select the capacitor first as there are fewer selections available. Stay above 1nF to avoid interactions with the wires/traces.
• Keep power supply lines away from signal lines to prevent inductive coupling. Try to solder the power wires to the board perpendicular to the input lines.
• A 1-10ohm resister between signal ground and real ground can help block ground noise coming up into the circuit. Some say add a torroidal choke also (wouldn't this block signal HF to ground???).
• A linear pot + shunt resistor presents a varying impedance to the input while a stand alone log pot does not.
• Loads. Capacitive loads have the current leading the voltage. Inductive loads have the current lagging behind the voltage. The difference between the two is the phase angle.
• Phasing problems mess with power output (math of Ohm's Law). If current lags behind voltage and voltage drops to zero while there are still watts mathematically present, current can go through the roof. This can destroy parts not rated for it.
• Speakers. Speaker impedance often rises with frequency. The higher impedance will reduce the effective output power for that frequency range.
• Speakers. Cabinet bracing options. Add braces behind the speaker mounting screws to the back of the cabinet? Same for the back of the driver? Helps stop resonating even more?
• Speakers. When trying to tune a cabinet, a freezer bag full of a determined amount of sand can be used to remove volume space and adds some damping.
• Peak Power Rating and Dissapation. Example 100watt amplifier into 8ohm speaker. RMS voltage: P = (V^2)/R, solve and multiply that by sqrt(2) for peak voltage (40v here). To find amps, use V=IR (peak amps is 5). 40v and 5amps are the peak values into a resistive load (in phase). Since P = V * I, peak wattage is 200w. Impedance dips in speakers and phasing problems can create some odd combinations and some even higher peaks. While the worst case is unlikely, it should be prepared for to avoid equipment damage or underrating. Normal worst case is phase from 45-60 degrees. At 45 degrees phase, double the normal wattage can can be wasted as heat and the speaker only gets half its power. The extra wattage doesn't go into the speaker but gets turned into heat inside the unit/chip since voltage has already changed and the amperes are too much given the new voltage (like a resistor). On the flip side, if the voltage goes up and the current lags behind in a sagging mode, the power to the speaker will be less. This is called Power Factor. It is calculated by cos(phase_angle) and determines the heat the amp dissipates and the power the load receives. (???calculations??? 45deg: amp=2x, spk=0.5x; 60deg: amp=1.66x, spk=0.24x; 90deg: amp=4x, spk=0x.) In general, take the average desired wattage and multiply it by 4. Be warned that parts rated for a wattage are done so at room temperature and the SOA (Safe Operating Area) quickly drops as temperature increases. Low frequency phase shifts cause far more problems than the high frequency (lower energy) ones.
• Isolate input and output plug's grounds from the chasis.

Misc
• Wikipedia: Hydraulic Analogy
• Electrons and Holes. Electrons come out of the negative terminal and are attracted to the positive terminal. Holes come out of the positive terminal and are attracted to the negative terminal.
• If a mu-metal cannot be used for magnetic shielding, gluing video tape to the case can be used as a work around.

Equations
• Digital Noise Floor: 20 * Log10 (2^16). For 16 bit.
• Filter RC -3db Point: Freq = 1 / (2 * PI * R * C)
• Baxandall: (requires low impedance input)
  Bass starting point: Fb0 = 1 / (2 * PI * C * R_pot)
  Bass 3db point: Fb1 = 1 / (2 * PI * C * R_to_pot_wiper)
  Treble: 1 / (2 * PI * C_treble * R_to_pot_wiper). Treble point interacts with the bass pot and shifts accordingly.
• Butterworth/Sallen-Key Filter. Freq = 0.707 / (2 * PI * R * C). The larger capacitor is twice C. Both resistors should be matched. 4C would form a Chebychev filter with Q=1. 1C would form a sub-Bessel filter with Q=0.5. It's usually easier to parallel capacitors and series resistors to get the 2x values necessary.
• Ohm's Law: V = I * R
• Power: P = V * I, P = (V^2)/R.
• Capacitor sizing for load current and ripple: C=(I_load / V_ripple) * k * 1mF. k=6 for 120Hz, 7 for 100Hz.
• BJT Equation Gain: Common emitter voltage gain = beta * (Rout/Rin). Rout is the load resistor. Rin is the base resistor.