In small signal analysis of diode (silicon) we take voltage drop
across diode (VD ) is 0.7 volt.
That's not quite correct. In small signal analysis, one linearizes about the operating point so, in fact, no assumption is made about the DC operating voltage - one should in fact solve for the operating point.
What is the significance of this voltage drop ? Does it add up with
0.7 voltage drop ?
No, to see the significance, let's review small-signal analysis. First write the total diode voltage as the sum of a constant and a time varying component:
$$v_D = V_D + v_d $$
where \$v_D\$ is the total voltage,\$V_D\$ is the DC (time average) voltage, and \$v_d\$ is the AC voltage.
Next we assume that the total voltage is at all times not very different from the time average which allows us to do small signal analysis in the first place.
The following is the justification for this approach.
The ideal diode equation is (assuming significant forward diode current)
$$i_D = I_S e^{\frac{v_D}{nV_T}}$$
Setting \$v_D = V_D + v_d\$ in the above yields
$$ i_D= I_S e^{\frac{V_D + v_d}{nV_T}} = I_S e^{\frac{V_D}{nV_T}}e^{\frac{v_d}{nV_T}} = I_De^{\frac{v_d}{nV_T}}$$
where \$I_D\$ is the DC diode current.
Expanding the exponential in a Taylor series yields
$$i_D = I_D (1 + \frac{v_d}{nV_T} + \frac{1}{2}(\frac{v_d}{nV_T})^2 + ... )$$
Now, here's the crucial move. If we assume \$v_d\$ is small enough, we can ignore the 2nd order and higher terms in the expansion yielding
$$i_D \approx I_D (1 + \frac{v_d}{nV_T}) = I_D + \frac{I_D}{nV_T}v_d = I_D + \frac{v_d}{r_d} = I_D + i_d$$
where
$$r_d = \frac{nV_T}{I_D}$$
Thus, assuming \$v_d\$ is small enough, this linear model gives good agreement and allows us to find the total diode current by superposition of the DC current and the small-signal current.
As it is a resistance there must be a voltage drop across it which is
nVt
It isn't a resistance. As shown above, \$r_d\$ is the ratio of the small-signal voltage \$v_d\$ to the small signal current \$i_d\$ which means
\$r_d\$ is the inverse slope of the diode IV curve at the operating point; it is the dynamic resistance at the operating point.
Best Answer
Both diodes are opposing therefore they block current in either direction therefore neither diode is forward biased. You do actually need current to flow to get any meaningful forward bias situation.
Of course there might be leakage currents (25 nA for the 1N4148 at 25 volt reverse voltage) but these are so small that the relevance of considering if one or the other diode was forward biased is lost. For instance if you looked at the 1N4148 forward characteristic you'd see something like this: -
At 100 uA, the forward voltage is about 0.5 volts and the voltage will drop at a rate of about 0.1 volt for each decade reduction in current hence, with 0.4 volts applied, I would expect the current to be 10 uA. For 100 nA I would expact the terminal voltage to be only 0.2 volts and 0.1 volts at 10 nA.