EE4609
Spring 2009
Homework #4
1) A driver is connected to two receivers via transmission lines. The circuit is shown below.
The driver voltage is a step voltage given by
0 t < 0
Vs(t) =
Vo t ³ 0
The driver internal impedance is RS = Zo. The receiver impedances are RL2 = Zo and RL3 = ¥. Each driver is connected to a transmission line of characteristic impedance Zo with a propagation delay of td1/4 where td1 is the prop delay for the main line.
Calculate and plot the voltage. VL2(t), across RL2 versus time for 0 £ t £ 3.25td1.
2) A driver sends out two pulses to a receiver on the circuit shown below.
The driver voltage, VS(t), is
The driver impedance is RS = Zo/4. The line has a characteristic impedance of Zo and a prop delay, td. The receiver impedance is RL = 9Zo.
Calculate and plot the receiver voltage, VL(t), versus t for 0 £ t £ 7td.
3) A driver produces ramp voltage given by
0 t < 0
Vs(t) =
Vo (t/tr) 0 £ t £ tr
Vo t > tr
where tr = td. The interconnect circuit is shown below
The driver and receiver impedances are Rs = Zo/4 and RL = ¥. The line parameters are Zo and td.
Calculate and plot the receiver voltage, VL(t) versus t for 0 £ t £ 7td.
4) An interconnect contains a via to allow the circuit to change board layers. The via can be modeled by a series inductor of value L. The circuit is shown below.
The driver and receiver impedances are both Zo. The inductor is located in the middle of a transmission line of characteristic impedance, Zo and total prop delay, td.
Derive an expression for the receiver voltage, VL(t) versus t.
[Hint: The transmission line behind the inductor looks like an impedance Zo. That portion of the line and the inductor form a series RL impedance as far as any forward wave on the line in front of the inductor is concerned. Determine the forward wave voltage launched into the left hand portion of the line by the driver. At the junction, the total voltage, V’(t) is equal to the sum of the voltages across the inductor, VL, and the transmission line, V. Use Kirchoff’s voltage law to express those two voltages in terms of L , Zo and the current through the inductor, IL. Equate this to the forward and reflected waves on the transmission line at the (left of) the junction. Next express the inductor current, IL, in terms of the same forward and reflected waves. Use these two equations to derive a differential equation for V-, the reflected wave on the left hand transmission line. Solve for V- using the value of V-at t = td/2 as a boundary condition. Then find IL in terms of V+ and V-. Use this to determine the voltage, V, across the right hand portion of the line. This becomes the first forward wave launched into that portion of the line.]