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http://roymal.tripod.com/reverb.htm reverb2
=

Using Op Amps to Interface to Spring-type Reverb = Units

Copyright 1999
Roy Mallory
roym@world.std.com=20
Revised November, 2001

Although digital reverb units have achieved widespread use, the = spring reverb=20 is still popular in guitar amplifiers. Many such amplifiers use tubes = for their=20 sonic and overdrive characteristics, but for interfacing to a spring = reverb, the=20 monolithic op amp offers superior capabilities. This tech note, which = discusses=20 how to optimally interface a spring reverb to an op amp, is divided into = three=20 sections, one describing the drive circuit, another discussing the = optimal drive=20 level, and the final describing the signal-recovery circuit. In all = sections, an=20 Accutronics model 8DB2C1B or 8BB2C1B reverb unit is used as an = illustrative=20 example. The circuit design concepts presented here are equally = applicable to=20 other reverb units.
 

The Drive Amplifier

In a spring reverb, a solenoid (coil of wire) is used to generate a = magnetic=20 field that imparts vibrations to the unit's springs. As Ampere's Law = shows, the=20 strength of the field is proportional to the current through the coil, = not the=20 voltage across it. Yet, many reverb drive circuits produce a voltage = rather than=20 a current output. Why is this a problem? Well, the solenoid that = produces the=20 magnetic field is also an inductor, and the impedance of an inductor = rises in=20 direct proportion to the frequency applied to it. Therefore, given a = constant=20 voltage input, the current produced in, and the magnetic field produced = by, the=20 coil goes down in direct proportion to frequency. Mathematically, we can = express=20 this with a couple of simple equations:

where: zL =3D the coil's impedance

s =3D the complex frequency variable, j2p=20 f

L =3D the coil's inductance

RL =3D the coil's resistance

Using Ohm's Law, we see that the current in the coil is:

So, using a voltage-output amplifier causes the reverb to produce = less and=20 less output as frequency goes up, which is not at all what one needs. It = is the=20 higher frequencies that produce a good reverb sound, and if the drive = amp=20 doesn't provide much output at these frequencies, the signal-recovery = amp will=20 need more gain and thus produce more noise.

Fortunately, a standard op amp allows an ideal solution to this = dilemma. It=20 is very simple and inexpensive to implement a current-output = (technically=20 speaking, a transconductance) amplifier with an op amp. The fact that = the=20 8DBC1B's drive coil is not grounded makes the task especially easy. = Consider the=20 following circuit:

 

Any input voltage applied to the op amp's noninverting input appears = at its=20 inverting input as well. Thus, the current at the inverting node, and = therefore=20 through the reverb coil, is simply Vin/R1. So, we see that the circuit = produces=20 a current output in direct proportion to its voltage input. Two problems = must be=20 solved before the circuit is truly useful, however. First, we should = roll off=20 the stage's output at low frequencies, because they contribute nothing = to the=20 reverb sound; and second, as shown, this stage is unstable or marginally = stable=20 at best. To understand the cause of the instability, consider that = through most=20 of its frequency range, the op amp's open-loop transfer function = produces a=20 90o phase shift. The network formed by the inductance of the = reverb=20 unit and R1 also produces a 90o phase shift, causing a total = of=20 180o of phase shift around the feedback loop. The = modifications shown=20 in the circuit below solve both problems:

Capacitor C1 reduces the gain at low frequencies. Empirically, a 3 dB = point=20 for the R1, C1 network between 150 and 300 Hz seem about right. The test = circuit=20 uses a 62 ohm resistor for R1 and a 10 m F = capacitor=20 for C1. This combination produces a 3 dB point at about 260 Hz.

The network comprising C2 and R2 compensates the stage to make it = stable. To=20 see how, consider that at high frequencies, the inductive reactance of = the=20 reverb coil is high, and the capacitive reactance of C2 is low. = Therefore, at=20 high frequencies, R2 effectively becomes the feedback element, which = restores=20 phase margin to the circuit. To understand how to select R2 and C2, = let's solve=20 for the impedance, zf, of the feedback network formed by = these two=20 components and the reverb coil:

Looking at the denominator, we see it has the expected second-order = form. To=20 select C2, pick a frequency at which you would like the stage to break = out of=20 its rising feedback impedance to a constant one, using the standard = formula:=20

A frequency between 5 kHz and 10 kHz is appropriate for a guitar = amplifier.=20 The 8DB2C1B tank has an inductance of about 44 mH; the test circuit uses = a 0.01=20 m H capacitor to produce a break frequency of = about 7.6=20 kHz.

Component R2 is selected to produce an appropriate Q according to the = formula=20

A 2 KW resistor should produce a Q of = about 1, but=20 core losses will lower the Q to that of a maximally-flat response. With = these=20 components, the magnitude of the feedback impedance is:

Next, we must look at the noise performance of this circuit. Several = noise=20 sources exist. First, let's consider the effect of op amp voltage noise=20 (en). This noise source, which can range anywhere from 1 to = 20 nV/rt.=20 Hz for commonly available op amps, acts just like an input voltage. So, = the=20 current noise produced is simply en/R1. If we take a typical = op amp=20 noise of 5 nV/rt. Hz, this source causes output current noise of 0.08 = nA/rt.Hz=20 in the test circuit. The Johnson noise of R1 also contributes. The = output=20 current noise it produces is simply its Johnson noise divided by its = resistance.=20 For the test circuit, this noise is 0.016 nA/rt. Hz, which is 5 times = lower than=20 the noise caused by en. Therefore, we can ignore it. The = Johnson=20 noise of the reverb coil's resistance causes voltage noise at the output = of the=20 op amp, but no current noise, so it too can be ignored.

The current noise at the noninverting input of the op amp produces an = input=20 voltage that is simply the product of the current noise times the output = impedance of the previous stage. This noise divided by R1 is the output = noise=20 from this source, so io =3D inRout/R1. If the = previous stage=20 had an output impedance of 20 kW , which is = not=20 uncommon for a tube stage, and if one used a bipolor-input op amp whose = input=20 current density were 1 pA/rt. Hz, which is typical of many such op amps, = the=20 output current noise would be about 0.3 nA/rt. Hz in the test circuit; = this=20 would be the dominant noise source. The lesson is clear: drive the stage = from a=20 low impedance or use a JFET-input op amp. Such amps typically have = current noise=20 densities of about 0.01 pA/rt. Hz. If either approach is taken, the = noise from=20 this source will be so low that it can be ignored. Op amp current noise = at the=20 inverting input simply goes into the reverb coil. This noise is also = much lower=20 than that caused by en, so it too can be ignored. Thus we see = that in=20 a properly designed stage, the op amp voltage noise is the only = significant=20 noise source.

What signal-to-noise ratios can be expected from such a stage? Let's = say we=20 choose an op amp whose voltage noise is 5 nV/rt. Hz, because such amps = are cheap=20 and easy to find. Let's assume a bandwidth of 10 kHz, which is = conservative,=20 because most guitar speakers don't produce much output beyond 5 or 6 = kHz. Almost=20 any op amp can put out 10 to 20 mA peak; let's be conservative again and = assume=20 that our stage can put out 7 mA rms. A quick calculation (peak rms = output=20 divided by the product of the noise density times the square root of = bandwidth)=20 shows a maximum signal-to-noise ratio of 119 dB!

Follow these simple design guidelines:

For good stability,

  • Choose R2 and C2 appropriately.=20
  • Properly bypass the supply voltages to the op amp.=20
  • Connect the ground side of R1 so that its current does not cause=20 unintended feedback paths.

For low noise:

  • Use the lowest input-noise op amp you can afford.=20
  • Use a JFET-input op amp, or drive the stage from a low-impedance = source.=20
  • Make sure that the stage is driven sufficiently hard to ensure = maximum=20 signal.

 

Designing For the Optimal Drive Level

Designing your drive amplifier so it can provide sufficient current = to the=20 reverb coil is a deceptively simple task. First, one must determine the = optimal=20 drive current that your particular model of reverb coil requires. = Unfortunately,=20 Accutronics' specifications can be a bit misleading. First, they publish = a=20 "nominal" drive level recommendation for their models. I'm not sure just = what=20 this number means, but I've concluded that it is best ignored. The = number they=20 provide that is meaningful is the maximum amp-turns that their drive = coils can=20 withstand before going into saturation. They spec this value as 25 = amp-turns=20 r.m.s.. Their use of an r.m.s. value here is also confusing, but let's = assume=20 they had sinusoidal excitation in mind, and therefore the peak current = value=20 would be 25*1.414 or about 35 amp-turns. I was able to verify by = experiment that=20 their drive coils (actually, of course, the cores of the coils) do go = into=20 saturation at about this level. So a design goal of a maximum drive = level of=20 about 30 amp-turns to allow for a safety factor seems about right.

To determine how much voltage we need to supply the reverb coil to = produce=20 current at this level, let's proceed simply and say that our guitar amp = should=20 be able to operate at full output up to 10 kHz. The 8DB2C1B's input coil = has 688=20 turns and an impedance of 310 ohms at 1 kHz. So, at 10 kHz the required = drive=20 voltage is

 A required drive level of 135 volts peak is not = encouraging, but do=20 we really need that much? Well, the highest note in a typical guitar is = the D=20 that is two octaves and a whole step above middle C. This note's = frequency is=20 1175 Hz. In addition, a string that is fretted that high doesn't put out = much=20 power in its harmonics. To add to the good news, a guitar puts out = maximum=20 volume when a chord and not just a single string is played. By = definition, all=20 other notes in any chord containing the high D must be lower in = frequency. So,=20 for an undistorted guitar, the reverb doesn't need any more headroom = than that=20 required to reproduce a 1 kHz signal at full blast. For the subject = reverb unit,=20 we are only talking about a 13.5-volt peak signal.

13 volts is cutting things close for an ordinary op amp, so one might = want to=20 use a high-voltage op amp if a higher-voltage supply is available or = switch to a=20 lower impedance reverb tank. An 8BB2C1B might be an obvious choice if = the latter=20 tactic is used. Its drive coil has 538 turns and an impedance of 190 = ohms at 1=20 kHz. To drive it fully at 1 kHz requires

Note however, that the tanks require 44 mA and 56 mA respectively to = drive to=20 peak level. Therefore a high-current op amp of some sort is required. = I've found=20 that an OPA551 works very nicely and can also take supplies up to =B1 30 volts for those who want extra headroom or = who are=20 amplifying signals with more high-frequency content.

If you would like to use the 8BB2C1B tank, the drive-circuit = component values=20 can be changed to the following:

R1 =3D 56 ohms

R2 =3D 1.6k

C1 =3D 20 uF

C2 =3D .033 uF

The attentive reader will note that the requirements discussed above = were for=20 an undistorted guitar. If a heavily distorted guitar signal is fed into = the=20 reverb tank, the amount of drive voltage required will increase = substantially,=20 because the clipped guitar signal contains much more power at higher=20 frequencies. Interestingly enough, not being able to reproduce the hard = edges of=20 a clipped guitar signal doesn't sound objectionable to my ears. It just = means=20 that the reverb part of the amplifier's output will sound a bit softer = and less=20 distorted than the main signal. I kind of like that, but another = listener may=20 not.

Signal-Recovery Amp

The most basic decision for this stage is whether to use an inverting = or=20 noninverting topology. The noninverting topology shown below is = preferred=20 because it allows the values of the gain-setting resistors to be = optimized for=20 lowest noise while allowing the input resistance of the stage to be set=20 independently.

The schematic above shows all the necessary circuit elements. = Resistors R1=20 and R2 set the gain of the stage. The requisite gain will depend on the = rest of=20 the system's gain, but gains between 50 and 100 are common. The test = circuit=20 uses a gain of 101, with R1 set at 68 ohms and R2 set at 6.8 kohms. The = value of=20 C1 is chosen to roll off the low-frequency gain of the circuit. The test = circuit=20 uses a 10 m F capacitor, producing a 3 dB = point of=20 about 230 Hz. There is considerable leeway in the selection of the 3 dB=20 point-let your ears be the guide. C2, which is 1500 pF in the test = circuit, and=20 R2 form a low-pass filter at 15.6 kHz; with such high gain, it is a good = idea to=20 keep possible out-of-band noise from subsequent stages.

The inductance of the reverb unit's pick-up coil will resonate with = the=20 capacitance of the coil's winding plus the capacitance of the shielded = cable=20 used to connect the coil to the circuit. In the case of the 8DB2C1B = unit, a=20 short cable will produce a resonance above 20 kHz, and R3 is not needed. = For=20 other units, or if a long cable is used, the resonance can move into the = audible=20 range. R3 can be used to damp this resonance. Its value can be = calculated using=20 the equation presented earlier for determining Q. Alternatively, it may = be=20 easier to determine its value empirically by checking for an impedance = peak.=20

Some designs call for placing a capacitor across the reverb unit's = output to=20 purposely place the resonance at some audible frequency. Although this = technique=20 does produce more output at resonance, it does so at the expense of = raising the=20 input impedance at that frequency. In my experience, any increase in = output is=20 more than offset by an increase in noise. In addition, the response = emphasis is=20 not pleasant to this author's ears. For lowest noise, it is best to damp = any=20 in-band resonance with R3.

The most important consideration for the design of this stage is low = noise.=20 As previously stated, the stage needs quite a bit of gain. As we did for = the=20 drive circuit, let's investigate all the noise sources. First, the = Johnson noise=20 of the reverb unit's output coil is connected directly to the stage's = input and=20 will be amplified along with the signal. The 8DB2C1B has an output = resistance of=20 200 ohms. The Johnson noise of this resistance is 1.8 nV/rt. Hz. In the = test=20 circuit, this resistance will cause output noise of 181 nV/rt. Hz.

The Johnson noise of R1 will be amplified by the R2/R1 ratio. = Therefore, R1=20 must be kept smaller than the resistance of the reverb coil if it is not = to add=20 appreciable noise. Because noise sources add in an r.s.s. (root sum = squared)=20 way, if R1 is less than one-third the value of the reverb coil's = resistance, the=20 noise it will add will increase the total noise by less than 1 dB. The = 68 ohm=20 resistor used in the test circuit meets this criterion. Note, however, = that some=20 resistors have noise considerably in excess of Johnson noise. Carbon = composition=20 units are notorious in this regard and therefore shouldn't be the first = choice=20 for R1. The Johnson noise of R2, because it is not amplified, is = negligible.=20

Because impedance at the noninverting node of the op amp is low, op = amp=20 current noise at this input causes negligible output noise. Current = noise at the=20 inverting input is multiplied by the value of R2. Still, this noise = source will=20 also be negligible, even for a bipolar-input op amp. Finally, the op = amp's=20 voltage noise is amplified along with its signal. Unless one uses a very = quiet=20 amp, this noise will be higher than the Johnson noise of the reverb = coil, and so=20 will be the dominant noise source of the stage. If an op amp with an=20 input-referenced voltage noise 5 nV/rt. Hz is used, the total output = noise of=20 the stage is about 540 nV/rt. Hz. Over a 10 kHz bandwidth, total noise = is about=20 60 mV r.m.s., quite a respectable figure. =

In many designs, the reverb unit is attached so it does not = electrically=20 contact the amplifier's chassis. As such, no ground loops will be = produced. If,=20 however, the reverb unit electrically contacts the chassis, the ground=20 connection at the op amp input may have to be eliminated to avoid hum. = If so=20 required, break the connection marked with an "x" in the schematic.

Follow these simple design guidelines:

  • Choose R1 so that its value is not more than 1/3 of the reverb = tank's=20 resistance.=20
  • Choose C1 to roll off the low-frequency response around 200 to 300 = Hz.=20
  • If necessary, install R3 to damp in-band resonances.=20
  • Use the lowest voltage-noise op amp you can afford.=20
  • Break the ground loop if the reverb tank is connected to a = grounded part=20 of the chassis.

Conclusions

The test circuits have been auditioned by several guitarists, all of = whom=20 have pronounced the quality of the reverb to be excellent. I have seen = many=20 statements that claim that op amps should not be used for interfacing to = spring=20 reverbs because they are too noisy or are unsuitable in some other way. = I can=20 only assume that such statements are based on misconceptions or poor = circuit=20 design. I believe that this tech note shows conclusively that op amps = provide a=20 nearly ideal mate to a spring reverb. In the combination of performance, = size,=20 and cost, no other circuit element can do such a superb job.


 Return to=20 home page
 

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