Current through a diode - non linear?
(1) When the series resistance is "small enough" such that \$v_D \approx V_1 \$, the current approximately follows the exponential diode current equation.

(2) When the series resistance is "large enough" such that \$v_{R1} \approx V_1 \$, the current approximately follows the linear Ohm's law equation.

So, you should only expect the current to approximately follow the diode exponential equation when \$v_{R1} &lt;&lt; v_D\$.

This implies that you'll only see something resembling the exponential response for \$ V_1 &lt; 0.8V \$ or so.  



For this circuit, the diode current is given by:

\$i_D =  I_S \exp(\frac{V_1 - i_DR_1}{nV_T})\$

or

\$nV_T\ln(\frac{i_D}{I_S}) + i_DR_1 = V_1\$

If you stare at this awhile, you see that the series current is approximately linear when:

\$i_D &gt;&gt;  \dfrac{nV_T}{R_1}\ln(\frac{i_D}{I_S})\$