- #1
JessicaHelena
- 188
- 3
- Homework Statement
- Consider the diode D_1 shown in Fig 7-1.
The diode is a non-linear device with the following I-V characteristics:
##i_D = I_S \cdot (e^{\frac{v_D}{v_{TH}} - 1)##
where i_D is the current through the diode, I_S is the reverse bias saturation current, v_D is the voltage across the diode, and V_TH is the thermal voltage. Assume ##I_S = 8*10^{-12}## and ##V_{TH} = 20mV##.
Although the diode is a non-linear device, it can be modeled as a resistor for small signals. Calculate the numerical value of the DC bias current I_D in mA such that its small-signal resistance is 5 Ohms.
- Relevant Equations
- iD = ID + id
(i.e., total variable iD = DC output ID + small signal id)
also,
##I_D + \delta i_D \approx## (iD evaluated at v_D) + (derivative of iD evaluated at v_D)*##\delta v_D##
##I_D = ## (iD evaluated at v_D)
##\delta i_D = ## (derivative of iD evaluated at v_D) *##\delta v_D##
We are given that ##i_D = 8\cdot 10^{-12} (e^{v_D/20m} - 1)##
Hence ##i_D' = e^{50 v_D}/2500000000## and ##i_D'' = e^{50 v_D}/50000000##
Then I have that ##\delta i_D \approx\frac{ e^{50 v_D}}{2500000000} \cdot \delta v_D = \delta v_D / 5## Cancelling ##\delta v_D## from boh sides and solving for the v_D, I have that ##v_D = 0.400602##.
Plugging this value into the original function for iD, I can get I_D, which gives me 0.004. However, this is not right. What am I doing wrong?
Hence ##i_D' = e^{50 v_D}/2500000000## and ##i_D'' = e^{50 v_D}/50000000##
Then I have that ##\delta i_D \approx\frac{ e^{50 v_D}}{2500000000} \cdot \delta v_D = \delta v_D / 5## Cancelling ##\delta v_D## from boh sides and solving for the v_D, I have that ##v_D = 0.400602##.
Plugging this value into the original function for iD, I can get I_D, which gives me 0.004. However, this is not right. What am I doing wrong?