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Consider the circuit in picture, used to measure the voltage across diode and current flowing through it.

schematic

simulate this circuit – Schematic created using CircuitLab

With this circuit I do measure the exact voltage across diode (\$V\$) with voltmeter, nevertheless the current measured with ammeter (\$I\$) is not the current passing through the diode, since \$I=I_d+I_v\$.

To evaluate the error committed doing the approximation \$I=I_d\$, is it correct to see if $$V/I << R_v$$ ?

Infact, supposing in first place that the approximation \$I=I_d\$ is correct, and also interpreting the ratio \$V/I_d=V/I\$ as the "equivalent resistance" of diode, then, using the current divider, if \$R_d <<R_v\$, then the approximation is justified a posteriori.

In other words is it correct to interpret \$V/I_d\$ as the resistance of diode, and consider the diode equivalent to a resistor for this porpouse (i.e. to evaluate this approximation)?

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    \$\begingroup\$ you mean the diode killer circuit you have drawn \$\endgroup\$ – JIm Dearden Mar 13 '17 at 17:13
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    \$\begingroup\$ first sign of old age ;-) \$\endgroup\$ – JIm Dearden Mar 13 '17 at 17:17
  • \$\begingroup\$ Your voltmeter (which is really an ammeter) will have a characteristic ohms/volt figure so if you wanted you could model this resistance in but unless you're looking at nA - uA range of diode current a modern digital voltmeter will have very little loading effect. \$\endgroup\$ – JIm Dearden Mar 13 '17 at 17:21
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The bulk resistance of the diode is not V/Id but rather ΔV/ΔI The lowest value is reached at max rated current and is approx Rd=1/Pd [ Ω ] for Pd rating on package.

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Using the standard diode equation $$Idiode = Is * e^[qv/ktn]$$ and letting n be 1, the diode current will increase by 2.718X for every 0.026 volts increase in Vdiode.

For this idealized equation [n usually is not exactly 1], we know exactly the diode's linearized resistance: at 1mA, Rdiode is 26 ohms; at 0.1mA, Rdiode is 260 ohms; Rdiode is 0.026/Idiode(amps).

This equation also applied to the transconductance (the 'gm') of bipolar transistors and diffpairs; this exact predictability makes discrete design a very fun project.

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Yes, it is, so long as Rv is sufficiently large vs the diodes equivalent resistance. This assumption may have difficulty to hold when thee current is very small, like ua or less.

I would put a resistor in serial with the diode as a precaution.

Edit, to give you a sense of how high the equivalent resistance can vary as the voltage across the diode changes.

For a typical small signal silicon diode like 1n4148, the equivalent resistance at 0v is about 25Meg. 400k at 300nv, 2k at 600mv and less than 1k at 700mv.

edit 2: ltspice showed an equivalent resistance of 18Meg @ 0v.

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