Maxim > Design=20 support > App = notes=20 > Amplifier=20 and Comparator Circuits > APP = 864
Maxim > Design = support >=20 App = notes=20 > Digital=20 Potentiometers > APP 864

Nov 28, = 2001

Keywords: EPOT Applications: Gain = Adjustment in=20 Op-Amp Circuits
Related=20 parts

Download,=20 PDF format (84kB)

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APPLICATION NOTE 864

EPOT Applications: Gain Adjustment in Op-Amp = Circuits

Variable=20 gain amplifiers often use a mechanical potentiometer = to set=20 the gain. An example is a volume control dial. = However, when=20 the analog=20 signal path is digitally controlled, a digital=20 potentiometer might be used to control gain. This = article=20 discusses the use of the digital potentiometer to form = digitally controlled gain or filter blocks.=20

General

Throughout this discussion of digital=20 potentiometers, the term EPOT is used rather than = digital pot,=20 EEPOT or E=C2=B2POT. The term EPOT describes the Maxim = series of=20 volatile digital potentiometers, while the other terms = describe a variety of non-volatile=20 and volatile devices manufactured on one of several = different=20 processes. The specifics of how these different = processes=20 affect digital potentiometer performance are outside = the scope=20 of this article. While the equations given below can = be=20 applied to all digital potentiometer circuits, the = special=20 considerations relating to voltage=20 ratings, current=20 ratings are intended specifically for Maxim's EPOT=20 devices.

Even though the designer needs to = adhere to=20 the standard constraints associated with semiconductor=20 devices, (i.e., absolute maximum ratings) there are a = couple=20 of characteristics specific to EPOTs that the engineer = should=20 keep in mind when using them in op-amp circuits. =

One=20 of the first things to remember is that the tolerance = of the=20 end-to-end or absolute resistance=20 of digital potentiometers is usually specified for a = maximum=20 of =C2=B125% to =C2=B130%. This is mainly due to = process variations and=20 a technique for handling this is discussed throughout = this=20 article.

Additional things to consider are the=20 characteristics of the EPOT's "wiper". The "wiper" in = an EPOT=20 is effectively a string of CMOS=20 switches and will exhibit the typical characteristics. = Important specifications for the wiper include its = resistance,=20 the variation of its resistance, its maximum current = rating=20 and its temperature=20 coefficient. For example, the wiper resistance of the = MAX5400=20 is specified for a typical value of 250 =CE=A9 but = with a maximum=20 value of 800 =CE=A9. The absolute maximum current = rating of the=20 wiper (as well as the rest of resistor in the EPOT) is = 1mA.=20 Care should be taken not to exceed this current rating = as=20 excessive current can damage the device. Lastly, the=20 temperature coefficient for the wiper is typically = about=20 =C2=B1300ppm/=C2=B0C.

One final EPOT = consideration is how it will=20 behave near either extreme of the adjustment range. = For=20 example, when an EPOT is set to one of its higher or = lower=20 settings the ESD=20 structures, such as wiper characteristics, can begin = to=20 drastically affect performance. A general rule of = thumb is to=20 try and keep the EPOT set to between 10% and 90% of = full=20 scale.

In general, the principles described = here apply=20 to all of the EPOTs in the Maxim line. The 256 tap = EPOT has=20 been chosen for illustration purposes. Internally, an = EPOT is=20 viewed as a string of resistors with CMOS switches = "tapping"=20 off that string. In linear EPOTs the spacing along the = resistor string is even, in logarithmic=20 taper EPOTs, the spacing would be logarithmic. = Therefore,=20 an EPOT with a given number (m) of taps has one fewer=20 resistors (m-1). For the purposes of discussion in = this=20 article, the variable "n" refers to the absolute = setting of=20 the EPOT (i.e., 0 to 31 or 0 to 255 and so on) and "N" = refers=20 to the ratio of the setting of the EPOT to its maximum = value=20 (i.e., 0 to 1). For example, in a linear=20 taper EPOT with 256 taps a setting of n=3D89 would = give=20 N=3D0.3490, which is 89/255. "Re" refers to the total = end-to-end=20 resistance of the EPOT, thus an EPOT can be thought of = as 2=20 resistors with values N =C3=97 Re and (1-N) =C3=97 Re. = Furthermore, gain=20 equations are shown in this article as a function of = the=20 variable "N" as G(N). The total available range of = adjustment=20 is shown as G(0)<=3DG(N)<=3DG(1) or as=20 G(1)<=3DG(N)<=3DG(0), as applies.=20

Non-Inverting Configurations

Circuit 1 is a=20 non-inverting gain configuration using the EPOT as a = variable=20 resistor. In this circuit, the wiper is connected to = one side=20 of the EPOT effectively shorting out the (1-N) =C3=97 = Re side of=20 the device. As a result, the feedback current flows = through=20 wiper and the portion of the EPOT correlating to N = =C3=97 Re. This=20 circuit has a nice linear gain adjustment curve with = respect=20 to N, but some of the EPOT's characteristics give this = circuit=20 a few disadvantages.

3D"Figure

<= I>Figure=20 1a. Circuit 1.

One disadvantage is that = because the=20 feedback current flows through the wiper, its = resistance (and=20 that resistance's variance with temperature) as well = as its=20 maximum current rating (typically about 1mA) may limit = the=20 applications for this circuit. Another disadvantage is = that=20 the end-to-end resistance, Re, is a part of the gain = equation=20 causing the =C2=B125% tolerance of Re to contribute up = to a =C2=B125%=20 variance in the gain. Mathematically, the maximum = possible=20 contribution of a 25% error in Re to the overall gain = is 25%.=20 Of course, as the Re/Ri term in the gain equation = becomes=20 smaller and the "1" term begins to dominate the gain, = the=20 error as a function of the tolerance of Re becomes = smaller.=20

<= I>Figure=20 1b. Gain of circuit 1 with Re=3D50k and=20 Ri=3D10k.

Circuit 1 is suited for cost = sensitive=20 systems that can live with the somewhat loose = tolerance in=20 overall gain. As with many of the circuits seen here, = this=20 includes circuits like volume or brightness=20 control where the user is going to iteratively adjust = the=20 circuit according to personal preference. Another = useful=20 application would be in an automatic=20 gain control circuit where either digital or = analog=20 automatic gain control is used to make a gain = compensation for=20 a system output. For example, an APD=20 circuit may use either digital or analog automatic = gain=20 control to control the biasing of the photodiode with = high=20 accuracy. In such a circuit, the automatic gain = control=20 technique takes the tolerance of Re (in the EPOT) out = of the=20 equation.

Another possible configuration is = shown in=20 circuit 2. Here the wiper is connected to the high impedance=20 input of the op-amp using the EPOT as a sort of = variable=20 voltage divider. By connecting the wiper to this = high-Z input,=20 the only current that flows through the wiper will be = the=20 input bias current of the op-amp. This current is = typically=20 very small (usually between pA and uA) so that any = variance in=20 the several hundred =CE=A9 resistance of the wiper = will be=20 negligible.

3D"Figure

<= I>Figure=20 2a. Circuit 2.

In addition, the Re terms on = the top=20 and bottom of the gain equation cancel out leaving = just a=20 function of N. This removes the impact of end-to-end=20 resistance from the gain equation=20 altogether.

Unfortunately, this circuit has one = big=20 disadvantage. The gain adjustment is non-linear with = respect=20 to N. A plot of G(N) for circuit 2 is shown in Figure = 2. By=20 deriving the slope of G(N) as G'(N) =3D 1/(1-N)=C2=B2, = it can be seen=20 that the slope is also a function of N and therefore = isn't=20 even piecewise linear over a select range of N. In the = section=20 on Inverting Configurations, several ways to use this = circuit=20 and counteract its inherent non-linearity are=20 discussed.

3D"Figure

<= I>Figure=20 2b. G(N) for circuit 2.

Circuit 2 is = useful in=20 many of the same systems mentioned for circuit 1 = (i.e., audio=20 control, brightness control, AGC loops etc.). In = addition to=20 the applications seen in circuit 1, the lack of a = dependence=20 on Re and the resistance of the wiper makes this an = excellent=20 circuit for calibration adjustments. Also notice that = in=20 circuit 2, the gain steps are heavily concentrated = from 1 to=20 2, but that much higher gains are still possible. = While rare,=20 some calibration applications may call for a period of = high=20 gain followed by a period of very finely tuned low = gain. An=20 example might be in the measurement of air pressure in = a blood=20 pressure cuff. In such a system, when inflation is = initiated,=20 the pressure is very low and the measurement is = primarily used=20 to detect faults (high gain). Once the cuff is fully = inflated=20 the measurements are used to detect minute changes in = cuff=20 pressure vs. time. The AGC loop using circuit 2 can be = used to=20 optimize ADC=20 dynamic=20 range during blood pressure measurement. The = calibration=20 is done at production to compensate for mechanical and = sensor=20 deviations.=20

Inverting Configurations

The principles used = in the=20 non-inverting configurations can also be applied to = inverting=20 op-amp circuits. In circuit 3 the gain is simply the = apparent=20 resistance in the feedback path over the input = resistance.=20

3D"Figure

<= I>Figure=20 3a. Circuit 3.

This circuit has the benefit = of=20 having a linear gain adjustment as a function of N, as = shown=20 in Figure 3b.

<= I>Figure=20 3b. G(N) for circuit 3 with Re=3D50k and = Ri=3D10k.

This=20 circuit has the same disadvantages as those seen in = circuit 1.=20 It will have a slightly different dependence on the = tolerance=20 of Re because the gain equation is slightly different; = the=20 gain will vary as much as =C2=B125% as the tolerance = on Re varies.=20 This circuit is going to be useful in inverting = applications=20 similar to those already mentioned for circuits 1 and=20 2.

Just like circuit 2, circuit 4 is not = susceptible to=20 the disadvantages mentioned for circuits 1 and 3. = Because the=20 Re terms on the top and bottom cancel each other out = of the=20 gain equation, the gain depends only on N. As a = result, errors=20 in the absolute resistance are effectively cancelled = out in=20 circuit 4, making it attractive for use with EPOTs = that have a=20 wide tolerance for the end-to-end resistance. In = addition, an=20 op-amp's input bias current is usually in the range of = pA to=20 uA. With so little current flowing through it, the = wiper's=20 resistance, drift with temperature and maximum current = spec=20 will not be a factor in this circuit.

<= I>Figure=20 4a. Circuit 4.

The gain for this circuit is = shown=20 in Figure 4b. This circuit has the same drawback as = circuit 2,=20 its gain adjustment is going to be non-linear over the = entire=20 range of N. This inherently non-linear gain adjustment = does=20 not prevent this from being useful. This circuit will = fit very=20 well where an inverting amp is needed in the same = applications=20 as for circuit 2. For example, this might fit well in=20 applications with user feedback, such as volume = control or=20 display brightness control circuits and also in = calibration=20 circuits or AGC circuits.

<= I>Figure=20 4b. G(N) for circuit 2 with a 256 tap=20 EPOT.

However, some systems require even = gain steps=20 as a function of N. Below, two approaches are given = for=20 linearizing the gain of circuit 4.=20

Linearizing Circuit 4's Gain with Resistors

In = circuit=20 5, resistors have been added to the input path and the = feedback path to "flatten out" the plot of the gain. = In the=20 plot of G(N) for this circuit, both its gain and the = gain for=20 circuit 4 are shown. The last 50 points have been = omitted for=20 clarity. This plot shows how the gain curve can be = "flattened"=20 at the expense of adjustment range.

<= I>Figure=20 5a. Circuit 5.

By adding resistors to both = the=20 input path and the feedback path, the minimum gain = (where N=3D0)=20 is raised and the maximum gain (where N=3D1) is = lowered=20 effectively compacting the available gain range. For = example,=20 in the plot shown the gain can be adjusted from 1 to 3 = rather=20 than from the 0 to 255 corresponding circuit 4. =

<= I>Figure=20 5b. G(N) for circuit 5 with Ri=3D50k and Rf=3D100k = (yellow). G(N)=20 for circuit 4 is also shown (blue) for=20 illustration.

This circuit also has the = advantage=20 of connecting the wiper to the high impedance op-amp = input.=20 Additionally, while the gain is not going to be = perfectly=20 linear like circuit 3, any effects the wiper's = characteristics=20 have on performance are taken out of the equation by = greatly=20 reducing the current through the wiper.

The big = drawback to this circuit is that by adding Ri and Rf = to the=20 gain equation, the Re terms that were cancelled out in = circuit=20 4 cannot be cancelled out here. One advantage of = circuit 4 was=20 that the Re terms in the gain equation cancelled each = other=20 out making the large tolerance of the end-to-end = resistance=20 irrelevant. For circuit 5 however, the Re terms cannot = be=20 cancelled out and deviations in the end-to-end = resistance of=20 the EPOT will affect the overall gain. The exact = impact of=20 deviations in the end-to-end resistance will depend on = the=20 ratio of Rf and Ri to Re. Making Rf and Ri large with = respect=20 to Re can minimize this impact, but will hamper the = available=20 adjustment range. In the example used for the plot of = Figure=20 5b, a 25% increase in Re makes the minimum gain 0.88 = rather=20 than 1 and the maximum gain 3.25 rather than 3. A 25% = decrease=20 in Re makes the minimum 1.14 and the maximum 2.75.=20

A Design Example using Software Compensation to = Linearize=20 Gain

Most systems use a microcontroller to control = the=20 setting of the EPOT and therefore, the gain of the = circuits=20 here are usually controlled by software. In addition, = while=20 this article has used 256 step EPOTs for illustration, = many=20 systems only need 20 to 30 steps in the gain. Using = software=20 and a 256 step EPOT configured as shown in circuit 4, = 20 to 30=20 steps of linear gain adjustment curve can easily be=20 accomplished by using software compensation. A design = example=20 is shown here for a software compensated, inverting, = and=20 adjustable gain op-amp circuit.

The goal for = this=20 design is to have the following performance = characteristics:=20

No current through the wiper.=20
A linear gain adjustment curve with better than = 3%=20 error. This is better than 1 LSB=20 for a 32 tap EPOT.=20
Eliminate any dependence on absolute resistance = Re.=20

To meet these design requirements, the = following=20 steps are offered. The basic idea is to pick the = optimal=20 number of gain steps between the desired minimum and = maximum=20 gain.

1. Pick a maximum and minimum = gain. For=20 this example a minimum of 2 and a maximum of 10 was = chosen.=20 Empirical testing shows that this method works pretty = well for=20 gains of up to about 20.

2. Find the actual = possible maximum gain. The actual maximum gain is = the gain=20 that will be a solution to the equation

G(n) = =3D n/(256=20 - n) n=3D0,1,2...

For this example, solving for = a G(n)=3D10=20 gives n=3D232.72. Since only whole values of n are = available,=20 select n=3D233. The actual maximum gain is then = G(233)=3D233/(256=20 - 233) =3D 10.13.

3. Get the slope m. = The slope m=20 could also be called the step size, as it will = correlate to=20 the gain steps between values of n. The recommended = method is=20 to use the average gain change over the last 5 values = of n in=20 the range of interest. In other words,

m=3D=20 [G(n_max) - G(n_max = -5)]/5

The=20 decision to use the last 5 values is somewhat = arbitrary and=20 the designer is encouraged to experiment with other = values.=20 For this example, m=3D[G(233) - G(228)]/5=3D0.398. =

4.=20 Find the actual possible minimum gain and the = number of=20 steps. In order to be certain that the minimum = gain is a=20 possible solution to the line being created, the = equation for=20 y=3Dmx+b can be solved. Since a discrete system is = being used,=20 simply find the number of steps between the max gain = and the=20 expected min gain (chosen in step 1), where

max = steps =3D=20 [G(n_max) - G_min]/m.

For = this=20 example, max steps =3D [10.13 - 2]/0.398=3D20.4. Once = again, only=20 a discrete number of steps is available, so round up = the=20 result to increase the maximum number of steps to 21.=20 Therefore, the actual minimum gain is going to be 21 = steps of=20 0.398 each less than the maximum gain = or

Gmin=3D=20 G(n_max) - (max steps) =C3=97 m =3D 10.13 - = (21 =C3=97 0.398) =3D=20 1.772.

5. Get the intercept b. The value = for b=20 or the y intercept is simply the min gain.

The = result=20 is the equation

f(x)=3D0.398x + 1.772, where=20 x=3D0,1,2...21.

This equation can be used to = find the=20 values of n or the EPOT settings that are used to get = this=20 straight line gain curve. This is done by solving G(N) = =3D=20 n/(256 - n) =3D f(x). The actual implementation is up = to the=20 designer, but basically the options are to either use = a lookup=20 table or to solve for the value of n on the = fly.

A plot=20 of the gain for this example is shown below as a = function of=20 x.

Figure=20 6. Gain curve for software compensated = example.

The=20 deviation from the ideal straight line is plotted = below as a=20 percentage.

Figure=20 7. Deviation from ideal as a percentage.=20

Summary

In this article, simple EPOT = adjustable gain=20 block configurations have been discussed, along with = the=20 advantages and disadvantages of each. The EPOT has = important=20 characteristics that must be considered when being = used in a=20 design. One of the cleanest ways of preventing these=20 characteristics from limiting the performance of the = circuit=20 results in a non-linear gain adjustment curve, which = may not=20 be desirable. Finally, two ways of compensating for = that=20 non-linear curve are presented. This would allow the = EPOT to=20 be used in a way where many of its constraints are not = a=20 factor and linear gain is still = achievable.

Related parts =

MAX5400<= /TD>

256-Tap = SOT-PoT,=20 Low-Drift Digital Potentiometers in = SOT23

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Download,=20 PDF format (84kB)
APP 864: Nov 28, = 2001=20
AN864, AN 864, = APP864,=20 Appnote864, Appnote 864=20 =