Exercise 11 + abacus

Exercise 11 + abacus

par Alexandre Nicolas Lechartier,
Number of replies: 2

Dear Prof. Enz, dear TAs,

May I, please, ask some questions about exercise 11?

1) For the problem 1, to get the result given by the eq. 6, it is mentioned that we need to use an abacus. Would it, please, be possible to be referred to a slide of the course where the abacus to calculate X is?

2) It I understood every thing correctly, to use the abacus, I should first calculate x, and then use it to find the value of $I_{Bi(x)}$ for i in N. Is it correct?

3) For problem 2, could you, please, explain how to obtain the expression of $G_{mcrit}$ in eq. 16?

4) For problem 2, for eq. 18, could you please explain why we have to take $Q_L$ in account in the expression of $omega_0$? I would have though that $omega_0 = \frac{1}{\sqrt{LC}}$.

5) For problem 2, for eq. 21 & 22, could you please refer me to the lesson's slides from which I could understand the used formulas and the reasons to use them?

Thank you,

Alexandre

In reply to Alexandre Nicolas Lechartier

Re: Exercise 11 + abacus

par Hung-Chi Han,
1) The slide does not provide an abacus. However, if you are interested, you could have a look at Python Scipy module (link), which provides a function to calculate the modified Bessel functions of the first kind of the real order.

2) Yes! Once you calculate the normalized amplitude `x`, you can insert it to a Scipy's function mentioned in Ans. (1).

3) You need to solve it together with (13) and (14).

4) Because G_m = G_mcrit, you will need (13), (16), and (17) to get (18).

5) the factor `2` in the denominator of (21) is due to V_out = \DeltaV_1 -  \DeltaV_2. You could fine Ch10.1 slide 72 and 73 for (22).

I hope it helps.

Best,
Hung-Chi
In reply to Hung-Chi Han

Re: Exercise 11 + abacus

par Alexandre Nicolas Lechartier,
Dear Dr. Hung-Chi,

Thank you for all your answers!

5) I don't understand about the factor 2. Is the factor 2 in the denominator because V_out = \DeltaV_1 - \DeltaV_2, thus V_out has twice the noize level of a voltage source, so we normalize V_out by 2?

Best,
Alexandre