HLab–1

Technical Note — 6 Aug 2017

“The Response of Systems to Special Signals”

Lab Week: Week 6
Total Marks: 10
Contribution to Final Assessment: 3%
Grading: Lab is marked based on satisfactory completion of tasks. Attendance is compulsory.
Relevant Textbook Sections: 1.6

1 Learning Outcomes

After completing this lab, the students should be able to:

  • Understand how signals are distorted when the system response is affected by inertia, and to select signals suitable for system characterization.
  • Demonstrate the effect of sinusoidal signals on systems response.
  • Test the linearity of various practical systems.

2 Modules and Devices Needed

Audio Oscillator, Sequence Generator, Baseband Channel Filters (BBCF), Oscilloscope, Buffer Amplifier, VCO, and Frequency Counter.

3 Background

Step Response of System

The step response of a system is used to characterize, measure and specify “inertia”. It can be determined as the output of a system, with zero initial conditions, when a step function (a function that changes its state from 0 to 1) is applied. Here, we observe and investigate the step response for different systems.

Practical Considerations: From a practical point of view, knowing how the system responds to a sudden input is very important. For example, the most important consideration affecting the speed of a digital signal is the switching process to produce a change of state. The switching time can never be instantaneous in a physical system because of energy storage in electronic circuitry, cabling and connecting hardware. This energy lingers in stray capacitance and inductance, and cannot be completely eliminated in wiring and in electronic components. The effect is just like “inertia” in a mechanical system.

Impulse Response

The impulse response refers to the change in the output of the system in response to some external transient change. The impulse response of the system is its output when presented with a brief input signal, called an impulse. The impulse input is considered as an energy burst to a system. The idea is straightforward. The pulse width is reduced to an infinitesimal value while maintaining the product of amplitude and width constant. Naturally this implies a very large amplitude. The impulse function plays a central role as one of the fundamental signals in systems theory, with numerous ramifications. It is not possible to produce a perfect impulse to serve as input for testing and therefore a short width rectangular pulse is used as an approximation of an impulse.

Linearity of a System

The system is said to be linear if it satisfies the homogeneity (scaling) property

and also satisfies the additivity property

where and .

Practical systems have limitations like bandwidth and maximum amplitude that the output can achieve, etc. Therefore, systems may not be linear for all types of inputs. A system may treat some portion of the input of the signal or some frequency components of the system linearly.

4 Part 1: Step Response and Impulse Response of Different Systems

4.1 Introduction

We study the step and impulse response of different systems. The audio oscillator module can generate TTL (signals that take value of 0 or 5 volts) or analog sinusoidal signals of variable frequency. The TIMS BBCF module has four different channels which are considered as four different systems.

Fig.1

Figure 1: Task–1 Channel Step Response

4.2 Task 1: Step Response

WARNING: Yellow sockets are analog, while red sockets are TTL. Always, make sure that the connected sockets are compatible.

  1. Connect the circuit shown in Figure 1. Using the AUDIO OSCILLATOR, set the frequency value to minimum, by turning the knob fully counter-clockwise. Using the SCOPE SELECTOR in the bottom row of TIMS, connect the output in Figure 1 to the oscilloscope Channel X, and the output of the AUDIO OSCILLATOR to Channel Y. Adjust the time base to display no more than two transitions. On the BBCF, select Channel 3. Observe the channel response to a single transition (you can use scope trigger and other time base controls to display a LO to HI transition). When the response to a step excitation is settled, it yields the step response.
  2. Using the same setup, display the step response for Channel 2 of the BBCF. Notice the presence of oscillations and the relatively long settling time to the final value (sometimes known as ringing — a term that goes back to the days of manual telegraphy and Morse code).
  3. Now switch to Channel 4. Compare the time delay of the response with the other two channels (a convenient reference point to measure delay is the 50% amplitude).1
  4. Measure and compare the rise time of the three step responses. Show your readings to the tutor.

4.3 Task 2: Impulse Response

An isolated pulse can also be used as an alternative to using an isolated step as the excitation to probe the behaviour of the system. The pulse at the SYNC output of the sequence generator serves as input for this.

  1. Connect the circuit in Figure 2. Also, connect the TTL output of the Audio Oscillator to the TTL input of the Frequency Counter in the bottom row of TIMS. Set the Audio Oscillator to 0.8 kHz. Connect the BBCF input to the Sync output of the Sequence Generator as in Figure 2. Pull out the SEQUENCE GENERATOR and check that the on-board DIP switch is in correct position for a short sequence, that is, both are at the upper position. Select BBCF Channel 3 and display the output and input of the BBCF on the scope. Notice that the input consists of a periodic train of widely separated impulses. The output should appear as a fully formed delayed imitation of the input. Set the time base to display one pulse only. Set the Frequency Counter knob to 1s, and progressively increase the Audio Oscillator frequency to 1600 Hz and observe the effect on the pulse width and pulse interval. Note that the transitions are not affected. As you continue to increase the clock frequency, the flat top between transitions gets shorter, and ultimately disappears.
    • Record the clock frequency at which this occurs and show to the tutor at the end of this task.
  2. Progressively increase the clock frequency to 2500 Hz. Since the upgoing transition is unable to reach its final value, it is not surprising that the amplitude of the pulse gets smaller. Note the shape, and look for further changes as the clock frequency is increased over the range available on the Audio Oscillator (adjust the scope time base as needed).
    • Can you determine the “demarcation” pulse width, i.e., after which the response shape remains unchanging?
    • Record your observations and show at the end of this task.

  1. The rise-time of the step response is an indicator of the time taken to traverse the transition range. Various definitions can be found according to the application context. We use the frequently used 90% criterion which is the time taken by the output to reach the 90% of the steady state value. ↩

Code Index:

Sphere Index:

Misc Index: