EE215 – Circuits and Systems
Lab 01 – The Infinite Resistance Ladder
Objective
Record the objective and sketch the circuit in your notebook!
Explore properties of the infinite resistance ladder shown in Figure 1 via theory, computation,
simulation and measurement.
V1
V2
V3
R
V4
R
V5
R
R
R
R
R
R
RT
Figure 1: Infinite Resistance Ladder
Theory I
Record all derivations in notebook. Include appropriate circuit sketches.
Use Figure 2 to find the total resistance of the single ladder section at the right-end of the ladder (R1).
R
R
R1
Figure 2: The Last (Right-Most) Section of the Infinite Ladder
Use Figure 3 to derive an expression for the resistance of the two right-most sections (R2) in terms of
R 1.
R
R
R
R
R
R2
R
R1
R2
(a)
(b)
Figure 3: The Last Two Sections of the Infinite Ladder
Note from Figure 4 that the relationship between Rn and Rn – 1 is the same as that between R2 and R1.
Generalize your previous expression to obtain an expression for the relationship between Rn and Rn – 1.
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Use this expression and previous results to calculate and record values for R1, R2, and R3 for R =
1000 Ω.
R
R
Rn - 1
Rn
Figure 4: Relationship between Rn and Rn – 1
Computation
Include printed copies of all programs in your notebook.
These must be trimmed to fit and taped/pasted into your notebook.
Write a MATLAB/Octave function named ladder_n (the file name should be ladder_n.m) that takes R
and n as arguments and returns the value of Rn. Verify that it provides correct results for R1, R2, and R3
when R = 1000 Ω.
Write a MATLAB/Octave script named comp_01 (the file name should be comp_01.m) that uses
ladder_n to display R1 through R10 for R = 1000 Ω. Include these values in your notebook. Does the
resistance of the ladder appear to be converging to a single value as sections are added?
Simulation
Include printed copies of all circuit schematics (and plots) in your notebook.
These must be trimmed to fit and taped/pasted into your notebook.
One team member should be simultaneously constructing the circuit required for the Measurement
portion of the lab.
Use LTspice to determine the resistance of a 10 section ladder when R = 1000 Ω. (Copying and pasting
a single section of the ladder can greatly speed up the construction of the schematic.
Use LTspice to find voltages V1 through V5 (see Figure 1) for a 10 section ladder when V1 = 10 V.
Measurement
Draw the circuit that is being constructed. Record all measurements.
In the interest of time and due to the number of resistors required construct only a 5 section ladder and
measure the total resistance of the ladder.
Apply 10 Volts to the “left end” of the ladder and measure voltages V1 through V5 (see Figure 1).
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Theory II
You should know what to do by now!!!
For an infinite ladder, Rn will be equal to Rn – 1 (removing one section from the left end of an infinite
ladder should not affect the resistance). In your formula relating Rn and Rn – 1 replace both Rn and Rn – 1
with RT and then solve for RT in terms of R. (Note: You should obtain a quadratic equation for RT that
has two mathematical solutions. Only one solution will correspond to a physically possible value of
resistance.) Evaluate RT when R = 1000 Ω.
In an infinite ladder, we can remove the left-most section and still have an infinite ladder with
resistance RT this leads to the equivalent circuit shown in Figure 5. This circuit can be used to also
derive an expression for RT in terms of R. The equation will be equivalent to that derived earlier.
Use the equivalent circuit in Figure 5 to derive the relationship between V2 and V1 in terms of R and RT.
Substitute the expression for RT to obtain a relationship between V2 and V1 that does not involve either
RT or R. The ratio of Vn – 1 to Vn will be the same as that of V2 to V1. Use this to calculate V1 through V5
in the infinite ladder when V1 = 10 V.
V1
V2
R
R
RT
RT
Figure 5: Equivalent Circuit for the Infinite Ladder
Conclusions
Summarize all your important results. Compare simulated, measured and calculated/computed results.
Give reasons for differences between results.
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