DSP

1. AC ELECTRICAL CIRCUITS LAB
EXPERIMENT: 3 – Transient response of RL circuit for DC input
AIM:
 To study the step response of first order circuits.
 To understand the concept of the time constant.
APPARATUS REQUIRED:
Cathode Ray Oscilloscope
 Function Generator
 Digital Multimeter
 Connecting probes
THEORY:
First-order transient circuits are described by a first order differential equation. First-order circuits
contain a resistor and only one type of storage element, either an inductor or a capacitor, i.e. RL or
RC circuits.
For a step voltage/current source input, the output can be expressed as
𝑋(𝑡) = 𝑋(∞) + [𝑋(0) − 𝑋(∞)] × 𝑒−
𝑡
𝜏
Where, X(0) is the circuit response at t = 0, and X(∞) is the response at t = ∞. The parameter 𝜏 is
called time constant of the circuit and gives the time required for the response
i. to rise from zero to 63% (or 1 −
1
𝑒
) of its final steady value as shown in Figure 3.2(a),
ii. to fall to 37% (or
1
𝑒
) of its initial value as shown in Figure 3.2(b).
Therefore, the smaller the value of 𝜏, the faster the circuit response is,
For a RL circuit,
𝜏 =
𝐿
𝑅

2. AC ELECTRICAL CIRCUITS LAB
CIRCUIT DIAGRAM:
Figure 3.1
Figure 3.2
EXPERIMENT
For all the circuits, 𝑅 = 1 𝑘Ω, 𝐿 = 100 𝑚𝐻
1. For the circuits in Figure 3.1 using step voltage sources, derive the analytical
expression 𝑉𝑜𝑢𝑡(𝑡) for 𝑡 ≥ 0, when 𝑉𝑖𝑛(𝑡) = .
2. Sketch or plot 𝑉𝑜𝑢𝑡(𝑡) for each circuit.
SIMULATION
Build and simulate the circuits in Figure 3.1 using Multisim. Set the input voltage to
±5𝑉 with a frequency of 1 kHz. Display 𝑉𝑜𝑢𝑡(𝑡) on the oscilloscope. Compare this result
with the plot from discrete lab result.
REPORT
Prepare the report as per the guidelines provided.