My first thought was S = {1,2,3,...}. However, if I define R = { (x,y) | y = 1/x }, I have a total injective relation, so this doesn't work.
The second thought was to try S = {...,-3,-2,-1,0,1,2,3,...}. However, a total injective relation can also be found here. For example, if I do something...
Attempts for each item:
a) Since m=n if and only if m \leq n and n \leq m:
Equal(m,n) = \left( \neg Greater(m,n) \right) \wedge \left( \neg Greater(n,m) \right)b) Any natural number n multiplied by 1 is equal to n, so:One(n) = \forall k \left(M(k,n,k)\right)c) What I've attempted here is to...
Thank you for the reply. To try to answer your question:
The gain is basically formed by two factors:
A=\left ( \dfrac{v_{out}}{v_{in}} \right ) \left (\dfrac{r_{in}}{r_{in}+\dfrac{1}{j\omega C}} \right )
where v_s is the input voltage, r_{in} is the input impedance at TR1's base, and v_{in} is...
Homework Statement
This problem is adapted from the book "Transistor Circuit Techniques" by G. J. Ritchie.
Given the following circuit:
(1) Calculate the AC gain of the circuit, for frequencies where C1 and C2 can be considered as short-circuits.
(2) Sketch the low-frequency response due...
Thank you all for the feedback.
Following gneill's suggestion, I redid this problem delaying the approximations, and I got the expected result.
For reference, here is my new solution:
I'm going to start again from this point (which is right before I applied the R_B\gg r_e approximation):
v_{out}...
Thank you for the reply.
I didn't include R_{IN} in the calculations because, in the KCL equation for Node 1, I think I can just use the quantity i_{in} as the current going into Node 1 from the input source.
I could have written \dfrac{v_{in}-v_{be}}{R_{IN}} instead of i_{in} as the current...
Homework Statement
The attached figure shows a "shunt feedback amplifier" circuit, and its AC equivalent model.
Verify that:
r_T = \dfrac{v_{out}}{i_{in}}=\dfrac{-R_B}{1+\dfrac{R_B+r_\pi}{(1+\beta)R_C}}
(assuming R_B\gg r_e, where r_\pi=(\beta+1)r_e.)
Homework Equations
In the...