Log amplifier

A log amplifier, which may spell log as logarithmic or logarithm and which may abbreviate amplifier as amp or be termed as a converter, is an electronic <a href="/facts/Amplifier/pnRgxncC">amplifier</a> that for some range of input voltage 
 
 
 
 
 V
 
 in
 
 
 
 
 {\displaystyle V_{\text{in}}}
 
 has an output <a href="/facts/Voltage/EN2po6N2">voltage</a> 
 
 
 
 
 V
 
 out
 
 
 
 
 {\displaystyle V_{\text{out}}}
 
 <a href="/facts/Approximately/LvYHsXzq">approximately</a> proportional to the <a href="/facts/Logarithm/QeXaV97q">logarithm</a> of the input:

V
          
            out
          
        
        ≈
        K
        ⋅
        ln
        ⁡
        
          (
          
            
              
                V
                
                  in
                
              
              
                V
                
                  ref
                
              
            
          
          )
        
        
        ,
      
    
    {\displaystyle V_{\text{out}}\approx K\cdot \ln \left({\frac {V_{\text{in}}}{V_{\text{ref}}}}\right)\,,}

where 
 
 
 
 
 V
 
 ref
 
 
 
 
 {\displaystyle V_{\text{ref}}}
 
 is a <a href="/facts/Normalization_constant/KKTfybqr">normalization constant</a> in <a href="/facts/Volt/KF18MXP2">volts</a>, 
 
 
 
 K
 
 
 {\displaystyle K}
 
 is a scale factor, and 
 
 
 
 ln
 
 
 {\displaystyle \ln }
 
 is the <a href="/facts/Natural_logarithm/PnreKEzI">natural logarithm</a>. Some log amps may mirror negative input with positive input (even though the mathematical log function is only defined for positive numbers), and some may use <a href="/facts/Electric_current/Dc1xdnUX">electric current</a> as input instead of voltage.
Log amplifier circuits designed with <a href="/facts/Operational_amplifiers/hunKdYb9">operational amplifiers</a> (opamps) use the <a href="/facts/Exponential_function/ewlYxvR2">exponential</a> <a href="/facts/Current%E2%80%93voltage_relationship/wft425cq">current–voltage relationship</a> of a <a href="/facts/P%E2%80%93n_junction/CaKIdLPg">p–n junction</a> (either from a <a href="/facts/Diode/JyaoyGnk">diode</a> or <a href="/facts/Bipolar_junction_transistor/9BMcGv5Q">bipolar junction transistor</a>) as <a href="/facts/Negative-feedback_amplifier/zQSRBReJ">negative feedback</a> to compute the logarithm. <a href="/facts/Multistage_amplifier/D16Bgbpd">Multistage</a> log amplifiers instead cascade multiple simple amplifiers to approximate the logarithm's curve. <a href="/facts/Temperature/QyGe4gmj">Temperature</a>-compensated log amplifiers may include more than one opamp and use closely-matched circuit elements to cancel out temperature dependencies. <a href="/facts/Integrated_circuit/fjn6vg7C">Integrated circuit</a> (IC) log amplifiers have better <a href="/facts/Bandwidth_(signal_processing)/7eMDzfJI">bandwidth</a> and <a href="/facts/Noise_(electronics)/Izbv38Rr">noise</a> performance and require fewer <a href="/facts/Electronic_component/F3NBVv4Q">components</a> and <a href="/facts/Printed_circuit_board/muSR2p43">printed circuit board</a> area than circuits built from discrete components.
Log amplifier applications include:

<ul><li>Performing mathematical operations like <a href="/facts/Multiplication/VtcUjpNv">multiplication</a> (sometimes called mixing), <a href="/facts/Division_(mathematics)/FqLKNkmq">division</a>, and <a href="/facts/Exponentiation/pac6QY2g">exponentiation</a>. This ability is analogous to the operation of a <a href="/facts/Slide_rule/KzIEdWad">slide rule</a> and is used for:
<ul><li><a href="/facts/Analog_computer/3NhYoCML">Analog computers</a></li>
<li>Audio <a href="/facts/Synthesizer/NrmdVrPa">synthesis</a></li>
<li><a href="/facts/Measurement_instruments/gfkMHBNR">Measurement instruments</a> (e.g. <a href="/facts/Electric_power/w61ID9yQ">power</a> = current × voltage)</li></ul></li>
<li><a href="/facts/Decibel/0LyxAPXh">Decibel</a> (dB) calculation</li>
<li><a href="/facts/True_RMS_converter/P4V8geN0">True RMS conversion</a></li>
<li>Extending the <a href="/facts/Dynamic_range/zxcuI4Fn">dynamic range</a> of other circuits, used for:
<ul><li><a href="/facts/Automatic_gain_control/qY7qWtC7">Automatic gain control</a> of transmit power in <a href="/facts/Radio_frequency/aWku7h4R">radio frequency</a> circuits</li>
<li>Scaling a large dynamic range <a href="/facts/Sensor/RN8SXbjs">sensor</a> (e.g. from a <a href="/facts/Photodiode/152Rpk06">photodiode</a>) into a linear voltage scale for an <a href="/facts/Analog-to-digital_converter/8YYNsMFg">analog-to-digital converter</a> with limited resolution</li></ul></li></ul>
A log amplifier's elements can be <a href="/facts/Operational_amplifier_applications/m7VjdVDl">rearranged to produce exponential output</a>, the logarithm's <a href="/facts/Inverse_function/Tg5nnXlu">inverse function</a>. Such an amplifier may be called an exponentiator, an antilogarithm amplifier, or abbreviated like antilog amp. An exponentiator may be needed at the end of a series of analog computation stages done in a logarithmic scale in order to return the voltage scale back to a linear output scale. Additionally, signals that were <a href="/facts/Companding/zsfkwSzp">companded</a> by a log amplifier may later be expanded by an exponentiator to return to their original scale.

Log amplifier open-in-new

Log amplifier