Question

Compute the reference voltage for a fundamental log-amp, if it’s internal resistance=5MΩ.

(a) 0.5µv

(b) 0.05µv

(c) 5µv

(d) None of the mentioned

This question was posed to me in an internship interview.

My question is based upon Very High Input Impedance Circuit in portion Operational Amplifier Applications of Linear Integrated Circuits

Answer 1

To compute the reference voltage for a fundamental log-amp, we can use the following concept:

The reference voltage VrefV_{\text{ref}}Vref​ for a fundamental log-amp is related to its internal resistance RintR_{\text{int}}Rint​ and the thermal voltage VTV_TVT​ (approximately $26\text{mV}$ at room temperature):

Vref=VTRintV_{\text{ref}} = \frac{V_T}{R_{\text{int}}}Vref​=Rint​VT​​

Given:

• Rint=5 MΩ=5×106 ΩR_{\text{int}} = 5 \, \text{M}\Omega = 5 \times 10^6 \, \OmegaRint​=5MΩ=5×106Ω
• VT=26 mV=26×10−3 VV_T = 26 \, \text{mV} = 26 \times 10^{-3} \, \text{V}VT​=26mV=26×10−3V

Calculation:

Vref=26×10−35×106V_{\text{ref}} = \frac{26 \times 10^{-3}}{5 \times 10^6}Vref​=5×10626×10−3​ Vref=5.2×10−9 V=5.2 μVV_{\text{ref}} = 5.2 \times 10^{-9} \, \text{V} = 5.2 \, \mu\text{V}Vref​=5.2×10−9V=5.2μV

Since none of the options exactly matches 5.2 µV, the most reasonable approximation would be (c) 5 µV.