Primary programmable rheostats
For a lot of variable resistor (rheostat) purposes, one of many system’s terminals is related to a voltage supply VS. Such a supply could be a reference DC voltage, an op amp output carrying an AC plus DC sign, and even floor. If free of the constraint of (programmable) “floating” rheostats happy by just lately disclosed options in “Synthesize precision Dpot resistances that aren’t within the catalog” and “Synthesize precision bipolar Dpot rheostats,” there’s a compelling various method. Sure, it’s barely less complicated in that it avoids MOSFETs, and that the +5V provide for the digital potentiometer is the one provide wanted (particularly if rail-to-rail enter and output op-amps are employed.) However extra importantly, it’s distinct in that it reveals no crossover distortion when there’s a change within the signal of an AC sign between terminals A and VS.
Wow the engineering world together with your distinctive design: Design Concepts Submission Information
As seen in Determine 1, I’m shamelessly appropriating the identical digital pot utilized in these different options. (Word the restricted working voltage vary of potentiometer U2.)
Determine 1 A primary programmable rheostat leveraging the identical digital pot utilized in different options.
The resistance between terminals A and voltage supply VS wanting into terminal A is res = R1/(1 – αa·α2·αb) the place the alphas are the positive aspects of U1a, U2, and U1b respectively. αa and αb are barely lower than unity at DC, falling in worth with loop acquire as frequency will increase. α2 is the same as one of many numerator integers 0, 1, 2… 256 divided by a denominator of 256 as decided by the programming of U2.
By altering the numerator from 0 to 255, it will seem that resistor worth ratios of 1:256 could possibly be achieved. Sadly, U2’s integral non-linearity (INL) is specified as ± 1 LSB. Strictly following this spec, operation with a numerator of 255 may drive the worth of res near infinity at DC and so needs to be prevented. However that’s not the one concern. For an α2 numerator worth “num”, a resistance error issue EF of roughly ± 1/(256-num) could possibly be encountered due to the ± 1 LSB accuracy. To attenuate uncertainty, num needs to be held to lower than some most worth (options in “Synthesize precision Dpot resistances that aren’t within the catalog” and “Synthesize precision bipolar Dpot rheostats” have comparable issues for small values of “num”). Another excuse for such a restrict is that resistance decision is a lot better with decrease than greater values of “num”. As an example, the ratio of resistor values with numerators of 10 and 11 is 1.004. However the values of 240 and 241 yield a ratio of 1.07, and people of 250 to 251, 1.2.
Enhanced programmable rheostat
The easy addition of U3 and R2 within the Determine 2 circuit mitigates these issues by lowering the required most worth of “num”. For R2 larger than R1, resistances between R1 and R2 needs to be applied by having analog change U3 choose R1 reasonably than R2. For bigger resistances, R2 needs to be chosen.
Determine 2 Enhanced programmable rheostat that mitigates the uncertainties issues of the fundamental programmable rheostat by lowering the required most worth of “num”.
To see why Determine 2 gives an enhancement, think about a requirement to supply resistance over the vary of 1k to 16k. In Determine 1 and Determine 2 circuits, R1 could be 1k. To provide a price of 1k, “num” could be 0. For 16k, “num” in Determine 1 could be 240, yielding a most EF of ± 1/(256 – 240) or roughly 6.3%. However in Determine 2, resistance values of 4K and above could be derived by having U3 change R1 out instead of a 4k R2. The utmost required worth of “num” could be 192, and EF could be diminished by an element of 4 to 1.6%. It would even be seen that the Determine 2 circuit considerably relaxes op-amp efficiency necessities for limiting the errors as a consequence of finite open loop positive aspects. To see this, some evaluation is important. Given the utmost allowed fractional resistance error (OAerr) launched by the op-amp pair, it may be seen that:
Subsequently, for closed loop op amp positive aspects:
At DC, op amp voltage follower closed loop acquire α is 1/(1-1/a0L), the place a0L is the op amp open loop DC acquire. To fulfill necessities at DC:
Enhanced programmable rheostat with AC indicators
Issues are extra difficult with AC indicators. At a frequency f Hz, the voltage follower open loop acquire HOLG(j·f) is 1 / (1/A0 + j·f/GBW), the place GBW is the half’s gain-bandwidth product and j = √-1.
The closed loop acquire HCLG(j·f) is 1/( 1 + 1/ HOLG(j·f)). Substitution of HCLG(j·f) for αa and αb in Equation (1) yields a fourth order polynomial as a result of actual and imaginary phrases of HCLG(j·f). It’s simpler to resolve the issue with a simulation in LTspice than to resolve it algebraically.
LTspice gives a user-specifiable op-amp known as…effectively, “opamp”. It may be configured for user-selected values of a0L and GBW. The software is configured as proven in Determine 3 to resolve this drawback.
Determine 3 LTspice can be utilized to find out op-amp necessities for an AC sign utility.
The a0L worth required for AC indicators shall be bigger than that calculated in equation (3). It’s instructed to begin with an a0L default worth of 10000 (100 dB) and take a look at completely different values of GBW. Use the outcomes to pick out an op amp for the precise circuit and both simulate it if a mannequin exists or not less than replace the simulation with the minimal specified values of a0L and GBW for the chosen op amp.
Desk 1 exhibits some examples of the behaviors of the circuit with completely different idealized op-amps. It’s clear that DC efficiency in both circuit will not be a problem for nearly any op-amp. But it surely’s additionally evident that the AC efficiency of a given op-amp is notably higher within the Determine 2 circuit than in that of Determine 1, and {that a} given error could be achieved with a decrease efficiency and less expensive op-amp within the Determine 2 circuit.
| Determine 1, R1 = 1k | Determine 2, R2 = 4k enabled | |||||||||
| num | 240 | 192 | ||||||||
| a0L, dB | 69 | 80 | 80 | 100 | 100 | 55 | 80 | 80 | 100 | 100 |
| GBW, MHz | 1 | 10 | 50 | 10 | 50 | 1 | 10 | 50 | 10 | 50 |
| DC resistance error as a consequence of op-amp pairs, % | 1.000 | 0.299 | 0.299 | 0.030 | 0.030 | 0.999 | 0.060 | 0.060 | 0.006 | 0.006 |
| 20kHz resistance error as a consequence of op-amp pairs, % | 15.952 | 0.495 | 0.307 | 0.227 | 0.038 | 2.024 | 0.071 | 0.060 | 0.017 | 0.006 |
| 20kHz part shift, levels | -30.22 | -3.42 | -0.69 | -3.43 | -0.69 | -6.71 | -0.69 | -0.14 | -0.69 | -0.14 |
| equal parallel capacitance at 20kHz, pf | 84.3 | 9.5 | 1.9 | 9.5 | 1.9 | 18.5 | 1.9 | 0.4 | 1.9 | 0.4 |
Desk 1 Examples of the circuits’ habits producing 16kΩ with varied op-amp parameters.
Word: The cascade of the 2 op-amps with their AC part shifts means that there’s an efficient capacitance in parallel with the resistance R created by the circuits. As a result of the 2 op-amps create a second order system, there isn’t any equal broadband capacitance. Nonetheless, a capacitance C at a spot frequency f Hz could be calculated from the part shift Φ radians at that frequency. C = tan(Φ)/(2·π·f·R). Simulations have proven that over the total vary of resistances and working frequencies of the examples listed in desk, part shift magnitudes are lower than 70 levels.
The method taken in Determine 2 could be generalized by supporting not simply two however 4 or extra completely different resistors. Doing so additional minimizes each op-amp efficiency necessities and worst-case errors by lowering the utmost required worth of “num”. It additionally extends the vary of resistor values achievable for a given error finances.
Christopher Paul has labored in varied engineering positions within the communications business for over 40 years.
Associated Content material
- Synthesize precision Dpot resistances that aren’t within the catalog
- Synthesize precision bipolar Dpot rheostats
- Error evaluation and mitigation of an revolutionary information acquisition entrance finish
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