Log Amp
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Log Amp

Description

The intent of this circuit is to compute log(v1/v2)

Design Details -- How It Works

The current through the collector of Q1, say IC1 is given by: IC1=IS*eVBE/VT           (1)
Where Is is the saturation current and VT is the thermal voltage. A little manipulation of (1) yields:
VBE = VT*ln(IC1/IS)            (2)

From the schematic, the input current to U1 is I=(V1-0)/R1; therefore, I=V1/R1    (3)
which is also the collector current of Q1. Now, since the base of Q1 is at ground, we have:

Vo1 = -VBE; so, from (2), vo1= -VT*ln(IC1/IS) and from (3), IC1 = V1/R1; therefore:

Vo1 = -VT*ln[ (v1/R1)/Is ]

Applying the same arguments to U2, we have:

Vo2 = -VT*ln[ (V2/R2)/Is ]

Applying Vo1 and Vo2 to U3 gives Vos=Vo2-Vo1; so:

Vos = -VT*ln[ (V2/R2)/Is ] + VT*ln[ (V1/R1)/Is ]
Vos = VT*( ln[ (V1/R1)/Is ] - ln[ (V2/R2)/Is ] )                   (4)

Recalling that ln(A/B) = ln(A) - ln(B), we can rearrange (4) as:

Vos = VT*ln[ (V1/R1*Is)/(V2/R2*Is) ]          (5)

Finally, since R1=R2 we simplify (5) to:

Vos = VT*ln(V1/V2)            (6)

At room temperature, VT = 25.3mV. Therefore, amplifying Vos by 1/.0253, will yield ln(V1/V2). However, our design requires that the circuit yield log(V1/V2). Recalling that log(x) = ln(x)/ln(10), we need to provide a gain of (1/.0253)*1/ln(10)=17.2. This gain is provided (approximately) by U4.

Diodes D1 and D2 protect Q1 and Q2 respectively from negative inputs. C1 and C2 prevent oscillations.

It should be noted that since VT is temperature sensitive, the accuracy of this circuit will be degraded by thermal drift. Also note that the analysis assumed identical thermal characteristics for Q1 and Q2; therefore, a matched pair such as is available in the CA3083 or other such similar device should be used.

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Copyright 2006-2017 kdkoadd
Page Last Modified: 10 January 2009

Fine print: Note that this site is intended as an information and education repository. Readers assume all risks and liabilities associated with the use of any information contained herein. The author assumes no liability of any kind for errors, omissions, or claims against any individual or corporation for use of the information contained herein.