# “Equivalent resistance” of diode as $V/I$ used to evaluate an approximation

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

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)?

• you mean the diode killer circuit you have drawn – JIm Dearden Mar 13 '17 at 17:13
• first sign of old age ;-) – JIm Dearden Mar 13 '17 at 17:17
• 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. – JIm Dearden Mar 13 '17 at 17:21

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.

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.

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.