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Em3rgent0rdr (talk | contribs) logarithmic converter is another spelling. Add about negative domain maybe mirroring positive output. Really just some range of the input, cause non-logarithmic things often happen near zero and there is always the question about negative inputs. |
Em3rgent0rdr (talk | contribs) →Drawbacks: add about how to deal with inputs around the size of Vt or smaller. |
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=== Drawbacks ===
The diode's saturation current <math>I_\text{S}</math> doubles for every ten [[kelvin]] rise in temperature. Similarly the emitter saturation current varies significantly from one transistor to another and also with temperature. Hence, it is very difficult to set the reference voltage for the circuit.<ref>[https://www.analog.com/media/en/reference-design-documentation/design-notes/dn288f.pdf RMS-to-DC Conversion Just Got Easy] Linear Technology, Design Note 288, 2002</ref>
Low-level voltages around the size of <math>V_\text{T}</math> or smaller are inaccurate. One approach is to use a symmetric function such as the [[inverse hyperbolic sine]], whose graph approximates log(2x) for large positive and log(–2x) for large negative values, but which linearly goes through 0 for small values. This function may be implemented with a combination of N and P diodes (sold many years ago in a temperature compensated module) to make what is called a "true log" amp or "baseband log" amp.<ref>{{Cite web |last=Nash |first=Eamon |date=March 1999 |title=Ask The Applications Engineer—28: Logarithmic Amplifiers Explained |url=https://www.analog.com/media/en/analog-dialogue/volume-33/number-1/articles/logarithmic-amplifiers-explained.pdf |url-status=live |archive-url= |website=[[Analog Dialogue]]}}</ref>
Additionally, the bulk resistance <math>R_{\text{B}}</math> of a real diode limits accuracy at high currents due to an added <math>I_{\text{D}} R_{\text{B}}</math> voltage term. Additionally, diffusion currents in surface inversion layers and generation-recombination effects in space-charge regions cause a scale factor <math>m</math> at low currents that varies (between 1 and 4) with current.<ref name=":3">{{Cite web |date=October 1987 |title=Linear Design Seminar (1987) Section 1: Analog Signal Processing: Analog Computation & Signal Processing |url=https://www.analog.com/media/en/training-seminars/design-handbooks/Linear-Design-Seminar-1987/Section5.pdf |pages=5-10}}</ref> With inputs near 0 volts, log amps have a linear <math>V_\text{in}</math> to <math>V_\text{out}</math> law. But this non-logarithmic behavior itself is often lost in this device noise, which limits the dynamic range to 40-60 dB, but the dynamic range can be increased to over 120 dB by replacing the diode with a transistor in a "transdiode" configuration.<ref name=":1">{{Cite web |date=2009 |title=MT-077 Tutorial: Log Amp Basics |url=https://www.analog.com/media/en/training-seminars/tutorials/MT-077.pdf |url-status=live |archive-url=https://web.archive.org/web/20221029071227/https://www.analog.com/media/en/training-seminars/tutorials/MT-077.pdf |archive-date=2022-10-29 |access-date=2023-06-28 |website=[[Analog Devices]]}}</ref>
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