The everyday anti-log circuit

The fundamental anti-log amplifier appears to be like just like the acquainted circuit of Determine 1.

Determine 1 The everyday anti-log circuit has uncertainties associated to the reverse present, I_s, and is delicate to temperature.

Wow the engineering world together with your distinctive design: Design Concepts Submission Information

The approximate equation for V₀ given in Determine 1 comes from the Ebers-Moll mannequin. A extra superior mannequin employed by many trendy spice simulators, corresponding to LTspice, is the Gummel-Poon mannequin, which I received’t focus on right here. It suffices for discussions on this Design Thought (DI) to work with Ebers-Moll and to let simulations profit from the Gummel-Poon mannequin.

The straightforward Determine 1 circuit is delicate to each temperature and the worth of I_s. Sadly, the worth and limits of I_s will not be laid out in datasheets. Curiously, spice fashions make use of particular parametric values for every transistor, however nonetheless say nothing in regards to the limits of those values. Transistors taken from totally different sections of the identical silicon wafer can have totally different parametric values. The variations between totally different wafers from the identical facility might be larger but and might be much more noticeable when these from totally different amenities of the identical producer are thought-about. Issue within the merchandise of the identical half quantity from totally different producers, and clear, believable issues about design repeatability are evident.

Addressing temperature and I_s variations

There’s a necessity for a circuit that addresses these two banes of constant efficiency. Fortuitously, the circuit of Determine 2 is a recognized answer to the issue [1].

Determine 2 This circuit addresses variations in each temperature and I_s. Key to its profitable operation is that Q1a and Q1b represent a matched pair, taken from adjoining areas on the identical silicon wafer. Working with the identical V_CEs can be useful for matching.

It really works as follows. Provided that Q1a and Q1b are taken from adjoining areas on the identical silicon wafer, their traits (and particularly I_s) are roughly an identical (once more, I_s isn’t spec’d). And so, we are able to write that:

It’s additionally clear that:

Moreover,

So:

Due to this fact:      

Substituting I_c expressions for the 2 V_BEs,

And right here’s a number of the circuit’s “magic”: no matter their worth, the matched I_s’s cancel! From the properties of logarithms,

Once more, from the properties of logarithms:     

Exponentiating, substituting for the I_c’s, and fixing for V₀:

Observe that V_i have to be adverse for correct operation.

Enhancing temperature compensation

Let’s now flip our consideration to utilizing a thermistor to cope with temperature compensation. These I’m used to coping with are adverse temperature coefficient (NTC) units. However they’ll do a poor job of canceling the “T” within the denominator of Equation (1). Was there an error in Reference [1]?

I exchanged the positions of R3 and the (NTC) thermistor within the circuit of Determine 2 and added a couple of resistors in numerous sequence and parallel combos. Making an attempt some resistor values, this met with some success. However the outcomes had been much better with the circuit as proven when a optimistic temperature coefficient (PTC) was used.

I settled on the available and cheap Vishay TFPT1206L1002FM. These are virtually completely linear units, particularly compared to the extremely non-linear NTCs. Determine 3 reveals the variations between two such units with resistances of 10 kΩ at 25°C. It is smart {that a} correctly located practically linear machine would do a greater job of canceling the linear temperature variation.

Determine 3 A comparability of a extremely non-linear NTC and a virtually linear PTC.

To see if it will enhance the general temperature compensation within the Determine 2 circuit, I thought-about including a hard and fast resistor in sequence with the TFPT1206L1002FM and one other in parallel with that sequence mixture.

Pondering intuitively that this three-component mixture would possibly work higher within the suggestions path of an inverting op amp whose enter was one other fastened resistor, I thought-about each the unique non-inverting and this new inverting configurations. The query turned the right way to discover the fastened resistor values.

The argument of the exponent in Equation (1) (unique of V_i) offers the switch operate H(T, <resistors, PTC>), which might be ideally invariant with temperature T (with Th1 suitably modified to accommodate the sequence and parallel resistors).

For any given set of resistor values, the configurations apply some approximate, common attenuation α to the enter voltage V_i. We have to discover the values of the resistors and of α such that for every temperature T_ok over a specific temperature vary (I selected to work with the integer temperatures from -40°C to +85°C inclusive and used the PTC’s related values), the next expression is minimized:

Excel’s Solver was the proper instrument for this job. (Drop me a notice on this DI’s feedback part should you’re within the particulars.)

The profitable outcome

The configurations had been discovered to work equally effectively (with totally different worth parts.) I selected the inverter as a result of it permits Vi to be a optimistic voltage. Determine 4 reveals the profitable outcome. The common worth α was decided to be 1.1996.

Determine 4 The simulated circuit with R_2a, R_2b, and R₃ chosen with the assistance of Excel’s Solver. A particular matched pair of transistors has been chosen, together with values for resistors R1 and Rref, and a voltage supply V_ref.

For Determine 4, Equation (1) now turns into roughly:

The circuit in Determine 4 was simulated with 10° temperature steps from -40°C to +80°C and values for V_i of 100 µV, 1 mV, 10 mV, 100 mV, 1 V, and 6 V. These V₀ values had been divided by these given by Equation (2), that are the anticipated outcomes for this circuit.

Over the commercial vary of working temperatures and greater than 4 orders of magnitude of enter voltages, Determine 5 reveals a worst-case error of -4.5% / +1.0%.

Determine 5 Over the commercial vary of working temperatures and over 4.5 orders of magnitude of enter voltages from 100 µV to six V, the Determine 4 circuit reveals a worst-case error of higher than  -5.0% / + 1.0%. V₀ ranges from 2.5 mV to three V.

Bonus

With a minor addition, this circuit also can help a present supply output. Merely cut up Determine 4’s R₁ into two resistors in sequence and add the circuit of Determine 6.

Determine 6 Cut up R₁ of Determine 4 into R_1a and R_1b; additionally add U₄, R_sense, and a 2N5089 transistor to supply a present supply output.

Caveats

 With all of this, the simulation doesn’t account for variations between the I_S’s of a matched pair’s transistors; I’m unaware of a supply for any such info. I’ve not specified op-amps for this circuit, however they may require optimistic and adverse provides and may have the ability to swing not less than 1-V adverse with respect to and have a common-mode enter vary that features floor. Bias currents mustn’t exceed 10 nA, and sub-1 mV offset voltages are beneficial.

Temperature compensation for anti-log amp

Excel’s Solver has been used to design a temperature-compensation community for an anti-log amplifier round a virtually linear PTC thermistor. The circuit reveals good temperature compensation over the commercial vary. It operates inside a sign vary of greater than three orders of magnitude. Voltage and present outputs can be found.

References

1. Jain, M. Ok. (n.d.). Antilog amplifiers. https://udrc.lkouniv.ac.in/Content material/DepartmentContent/SM_6aac9272-bddd-4108-96ba-00a485a00155_57.pdf

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