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2013-05-13T14:58:57Z

83.70.241.79: /* Case studies */

A '''log amplifier''' is an [[amplifier]] for which the output voltage ''V''out is ''K'' times the [[natural log]] of the input voltage ''V''in. This can be expressed as,

:<math>V_\mathrm{out} = K \ln\frac{V_\mathrm{in}}{V_\mathrm{ref}}</math>

where ''V''ref is the normalization constant in volts and ''K'' is the scale factor.

== Basic op-amp diode circuit ==

[[Image:Op-Amp Logarithmic Amplifier.svg|thumb|300px|Basic op-amp diode log converter]]

The relationship between the input voltage <math>V_{\text{in}}</math> and the output voltage <math>V_{\text{out}}</math> is given by:

:<math>V_{\text{out}} = -V_{\text{T}} \ln \left( \frac{V_{\text{in}}}{I_{\text{S}} \, R} \right)</math>

where <math>I_{\text{S}}</math> and <math>V_{\text{T}}</math> are the [[saturation current]] and the [[thermal voltage]] of the diode respectively.

 

== Transdiode configuration ==
[[Image:Logamp.JPG|thumb|300px|A transdiode configuration with a [[bipolar junction transistor|BJT]] connected in the negative feedback loop.]]
A necessary condition for successful operation of a log amplifier is that the input voltage, ''V''in is always positive. This may be ensured by using a [[rectifier]] and [[Electronic filter|filter]] to condition the input signal before applying to the log amp input. As ''V''in is positive, ''V''out is obliged to be negative (since the [[op amp]] is in the inverting configuration) and is large enough to forward bias the emitter-base junction of the BJT keeping it in the active mode of operation. Now,

:<math>V_\mathrm{BE} = -V_\mathrm{out}\,\!</math>
:<math>I_\mathrm C = I_\mathrm{SO}(e^{V_\mathrm{BE} / V_\mathrm T} - 1) \approx I_\mathrm {SO} e^{V_\mathrm{BE} /V_\mathrm T}</math>
:<math>\Rightarrow V_\mathrm{BE} = V_\mathrm T \ln \frac{I_\mathrm C}{I_\mathrm{SO}}</math>

where <math>I_\mathrm{SO}\,</math> is the saturation current of the emitter-base diode and <math>V_\mathrm T\,</math> is the [[thermal voltage]].
Due to the [[virtual ground]] at the op amp differential input,

:<math>I_\mathrm C = \frac{V_\mathrm{in}}{R_1}</math>, and

:<math>V_\mathrm{out} = -V_\mathrm T \ln \frac{V_\mathrm{in}}{I_\mathrm{SO} R_1}</math>

The output voltage is expressed as the natural log of the input voltage. Both the saturation current <math>I_\mathrm{SO}\,</math> and the thermal voltage <math>V_\mathrm T\,</math> are temperature dependent, hence, temperature compensating circuits may be required.

== See also ==

*[[Diode#Current–voltage characteristic|Diode]]
*[[Operational amplifier applications#Logarithmic output|Logarithmic output]]

== External links ==
*[http://www.maxim-ic.com/app-notes/index.mvp/id/3611 Integrated DC logarithmic amplifiers] from Maxim's AN 36211
*[http://books.google.bg/books?id=io36-F1cPu8C&pg=PA164&lpg=PA164&dq=transdiode&source=bl&ots=UeltPYWaC4&sig=4senZ5lkybZ4H-n36iEP_nccC7U&hl=en&ei=UVrDS7fMDuigOOHdqFA&sa=X&oi=book_result&ct=result&resnum=10&ved=0CCcQ6AEwCQ#v=onepage&q=transdiode&f=false Analog electronics with Op Amps] by A. J. Peyton, V. Walsh

[[Category:Electronic amplifiers]]

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