Lab 4: Special Signals TIMS

Lab 4: Special Signals TIMS   

 

Introduction 

The following lab introduces and extends our understanding of the TIMS software and PICO device practice. Bandwidth, in the context of signals and systems, refers to the range of frequencies over which a signal exists, or a system operates effectively. For signals, it defines the span between the lowest and highest frequencies present. For systems, like amplifiers or filters, it delineates the frequency range within which performance meets specified criteria, often characterized by a minimal attenuation or deviation from the desired response. The following lab, students will be introduced to the new modules: “AUDIO OSCILLATOR, SEQUENCE GENERATOR, BASEBAND CHANNEL FILTERS, and UTILITIES”.  Overall, the lab should extend the user's understanding of how signals interact with systems and their appreciation for material learned in class. 

 

Procedure 

Part A: Digital Pulse Sequence  

A.1 – The AUDIO OSCILLATOR  

1. Place the AUDIO OSCILLATOR module in slot 2 of the TIMS rack as depicted. 

2. Connect the AUDIO OSCILLATOR's TTL output to both the FREQUENCY COUNTER and Scope ChA. Adjust the AUDIO OSCILLATOR's 'f' knob to read 6.94 kHz (though "kHz" here refers to 1000 clock cycles per second, not sinusoidal cycles). 

3. Activate the PicoScope: 

• Set its time scale to 200us/div. 

• Use "single" for a snapshot view of the signal, called "Single Shot Triggering" 

• Deactivate the triggering and press the green triangle to restart the scope. 

4. Fine-tune the AUDIO OSCILLATOR to approximately 1kHz. Use the scope's single shot triggering to inspect the clock signal. 

5. Familiarize yourself with the PicoScope tools: 

• Arrow, hand, and magnifying glass icons are available. 

• The arrow reveals cursor details when clicked on a trace transition. 

• Use the magnifying glass for zoom, then the arrow for detailed readings. 

 

Duration of one pulse width and one clock cycle= .475ms, .996ms, respectively. 

 

A.2 – The SEQUENCE GENERATOR 

Using an external clock signal, the SEQUENCE GENERATOR produces two independent pseudorandom sequences, X and Y. These sequences can be accessed as standard digital (TTL) or analog outputs. 

6. Place the SEQUENCE GENERATOR in the TIMS rack, as in Figure 6's slot 4. 

7. As shown in Figure 7a: 

• Connect the AUDIO OSCILLATOR TTL clock signal to the SEQUENCE GENERATOR's red clock input, the FREQUENCY COUNTER, and Scope ChA. 

8. Link the SEQUENCE GENERATOR's red X output to the scope's channel B, as depicted in Figure 7a. 

9. On the PicoScope: 

• Activate ChB to Auto. 

• Set the time base to 1ms/div to better visualize the digital signal. 

• Use single shot triggering, shown in Figure 7b. 

10. Utilize the zoom and cursor tools to identify the shortest intervals between digital signal transitions. To recheck the smallest transition, repeatedly activate single shot triggering by clicking the green arrow next to the trigger. 

 

Minimum interval of the digital signal = 1ms 

 

Compares strikingly close to the clock cycle duration, almost the same. 

 

displayed portion of the digital signal to a binary code: 11100110000000011111 

 

 

Figure 1: Clock and Digital Signals 

 

 

A.3 – BASEBAND CHANNEL FILTERS 

The module offers a selection of four channels. Channel 1 provides a direct connection, whereas channels 2, 3, and 4 are unique low pass filters denoted as BBLPF2, BBLPF3, and BBLPF4. For a deeper understanding of these filters, refer to the appendix. In this experiment, the filters emulate limitations in response time, drawing parallels to the "system inertia" metaphor. Observations will focus on the digital signal before and after the filtering process. 

11. Position the BASEBAND CHANNEL FILTERS module in slot 6 of the TIMS rack, as illustrated in Figure 8. 

12. Establish connections based on Figure 8: 

• Consider starting afresh by detaching prior connections. 

• Link the AUDIO OSCILLATOR TTL clock signal to both the SEQUENCE GENERATOR's red clock input and the FREQUENCY COUNTER. 

• Connect the SEQUENCE GENERATOR’s TTL clock output to the BASEBAND CHANNEL FILTERS input and Scope ChA. 

• Route the Baseband Channel Filters OUT to Scope ChB. 

• Activate Channel 2 on the BASEBAND CHANNEL FILTERS module. 

13. Set up the PicoScope: 

• Adjust the time scale to 1ms/div. 

• Implement AC coupling for both channels A and B. 

• Activate Channel B and set its scaling to +/-5V. 

14. Monitor various single-shot trigger events, with an example presented in Figure 9. 

Understanding Transition Times: Digital signals transitioning between low and high states (and vice versa) have associated rise and fall times, collectively called "transition times." The rise time measures how long a signal takes to move from 10% above its baseline to 90% of its eventual stabilized voltage. Fall time is gauged similarly. Figure 10 illustrates these aspects, including the delay the system adds to the signal. 

15. Apply the acquired knowledge to gauge the delay, rise, and fall times of the digital signal as it traverses different filters. Ensure all measurements are at 1kHz. 

 

 

Table 1: channels delay rise and fall times 

 

16. Figure 13(a) and (b) display typical outcomes reflecting the delay and distortion caused by the low pass filter system. 

17. With BBLPF 4, adjust the Audio Oscillator's 'f' until the frequency counter indicates 2.0 kHz and examine the output, as illustrated in Figure 13c. 

18. Progressively raise the 'f' value and identify the frequency at which the digital signals of 1s and 0s become indistinguishable. 

 

At 4.7kHz you no longer able to accurately discern the digital signal when using BBLPF4  

 

 

Figure 2: undiscernible digital signal at 4.7kHz when using BBLPF4 

 

Part B – Step Input 

To determine system delay and response, a step function input is commonly used. This experiment simulates this function by examining the response to a prolonged pulse. 

19. Set up connections: 

• Link the AUDIO OSCILLATOR output to both the FREQUENCY COUNTER input and the BASEBAND CHANNEL FILTERS input, as portrayed in Figure 14. 

• Connect Scope ChA and ChB to the input and output of the BASEBAND CHANNEL FILTERS, respectively. 

• Minimize the 'f' setting on the AUDIO OSCILLATOR and select Channel 2 (BBLPF2) on the BASEBAND CHANNEL FILTERS. 

20. Observe the input and output signals using the PicoScope: 

• With a low 'f', you should notice one or two pulses. 

• Configure the PicoScope settings as detailed, including the time scale and output settings. Initiate several scans to get views akin to Figure 15a. 

• Zoom into a signal segment, resembling Figure 15b. The visual will represent the system's response to the step input. 

• This isolated step reaction is termed the "step response". It's essential to note the oscillations and extended settling time, termed "ringing", harking back to telegraphy days. 

21. Measure the system's delay: 

• Calculate the delay by determining the time at the 10% response point and subtracting the step's start time. Document this in Table 2. 

22. Ascertain the rise time using Figure 10 as a reference and record the outcome in Table 2. 

 

 

Table 2: continued table 1 

 

Part C – Impulse Analysis 

An ideal impulse is pivotal for indicating derivatives at discontinuities and the sifting function application. The system's reaction to this impulse (the "impulse response") is invaluable for linear time-invariant (LTI) systems. With LTI systems, any input can be represented as a series of impulse functions, making the response to the signal the sum of the responses to the impulse series. 

Though an ideal impulse is represented mathematically as a brief pulse, the TIMS experiment will approximate it using a limited-duration rectangular pulse. However, this pulse's height will have system constraints, meaning our impulse signals will cover an area less than 1, equivalent to giving the system lesser power. Referencing a voltage vs. time response, the system's impulse response will mirror the ideal impulse input but will be voltage compressed. 

23. Begin anew for clarity: 

• Detach all leads and deactivate the PicoScope. 

24. Utilize the SEQUENCE GENERATOR's SYNC output to approximate a single rectangular pulse: 

• Link the AUDIO OSCILLATOR TTL LEVEL OUTPUT to both the SEQUENCE GENERATOR's TTL CLOCK input and the FREQUENCY COUNTER's TTL input. 

• Connect the SEQUENCE GENERATOR's SYNC output to Scope ChA. 

• Fully rotate the 'f' counterclockwise on the AUDIO OSCILLATOR. 

25. Activate the PicoScope: 

• Set ChA to DC coupling. 

• Configure the Trigger to AUTO mode. 

26. Explore the connection between frequency and pulse width: 

• Position 'f' close to 0.5 kHz, measure the pulse width, document this, and plot it. 

 

 

Table 3: Pulse width data 

 

 

Figure 3: Fig 19 Relation between frequency and pulse width 

 

27. Attach the SEQUENCE GENERATOR's output to the input of the BASEBAND CHANNEL FILTERS. Then, connect the BASEBAND CHANNEL FILTERS' output to Scope ChB. 

28. Activate Ch B on the PicoScope using DC coupling at a range of +/- 10V. 

1. Adjust the AUDIO OSCILLATOR's frequency to 300 Hz 

29. Monitor the response as you gradually raise f to 1000 Hz. Refer to Figure 22. 

1. Observe that while the transitions remain unchanged, increasing the frequency and thereby decreasing the impulse width causes the flat top between transitions to become more abbreviated, eventually vanishing. 

30.     Elevate f to 2000 Hz.      

31. Gradually raise f from 2000 Hz to 10,000 Hz and watch the resulting change. 

It's worth noting that when the pulse width diminishes sufficiently, the overarching form of the output, excluding its magnitude, remains constant. This consistent pattern is the system's impulse response." 

 

Amplitude changes with a continuous decrease in pulse width because frequency increases. Input directly affects the output in a proportional manner. The system is designed, specifically in this manner. 

 

D.1 – Introduction to Sine Waves 

1. To ensure alignment between the following steps and your observations, it's advised to begin from scratch. 

- Remove all connections and power down the PicoScope. 

2. Link the AUDIO OSCILLATOR's sin(t) output to the BUFFER AMPLIFIER's input A.  

   - This BUFFER AMPLIFIER integration facilitates the manipulation of the sinusoidal wave's amplitude. 

3. Connect the BUFFER AMPLIFIER's output k1A to the FREQUENCY COUNTER, the input of the BASEBAND CHANNEL FILTERS, and Scope ChA.     

- Set the AUDIO OSCILLATOR's frequency to 300 Hz. 

   - Switch the BASEBAND CHANNEL FILTERS to Channel 2 (BBLPF2). 

4. Attach the BASEBAND CHANNEL FILTERS' output to Scope ChB. 

5. Launch the PicoScope software: 

   - Adjust the timescale to 1ms/div and set the Trigger mode to Auto. 

   - Activate Channel B. Start with the Auto Scale feature but be ready to modify the scaling as necessary. 

   - Fine-tune the BUFFER AMPLIFIER's gain using knob k1 to secure a 6 Vpp (indicating "6 volts peak-to-peak") input signal. 

6. Observe and note down the output signal's Vpp value in a table. 

7. Complete a table by tweaking the frequency and amplitude of the sinusoid: 

   - Ensure the input signal consistently remains at 6 Vpp. 

   - Modify the time scale as required to visualize multiple sinusoid cycles. 

 

 

Table 4: Vpp values for different frequencies 

 

As frequency increases, Vpp decreases. This can be correlated to signal quality based on the interpreter's definition of quality. 

 

Considering the signal's inherent noise, obtaining an exact Vpp measurement might prove challenging. It's advisable to measure from the midpoint of the unclear trace. 

 

D.2 – Exploring Clipping 

Next, we'll employ the UTILITIES module to demonstrate how the CLIPPER BIPOLAR OUTPUT (often referred to simply as the CLIPPER) can transform a sine wave into a square wave. 

  

1. To align the upcoming instructions with your observations, it's best to begin anew: 

   - Remove all current connections and shut down the PicoScope. 

2. Set up the circuit 

   - Link the AUDIO OSCILLATOR's sin(t) output to the BUFFER AMPLIFIER's input. 

   - Connect the BUFFER AMPLIFIER's ANALOG OUTPUT to the FREQUENCY COUNTER, to the ANALOG SIGNAL INPUT of the UTILITIES module, and to Scope ChA . 

   - Attach the CLIPPER to Scope ChB. 

3. PicoScope Configuration: 

   - Set the timescale to 1ms/div and position the ChA trigger to Auto mode. 

   - Calibrate BUFFER AMPLIFIER k1 to achieve an output of 6Vpp. 

4. Activate ChB on the PicoScope and match its scale to ChA. 

5. Refine the BUFFER AMPLIFIER's k1 setting to reduce the input signal to a Vpp between 300 to 350 mV: 

   - Utilize the Single Shot Triggering feature on the PicoScope. 

 

Output is more steady and greater amplitude than input signal 

 

6. Gradually amplify the signal to reach 20 Vpp.  

 

Output is more static, and amplitude is lower than input 

 

It's essential that the signal directed to the Comparator is sufficiently robust to activate the Clipper. 

 

E: Digital Signal Recovery 

When a digital signal traverses a system, like the BBLPF2, it can experience degradation. However, if this degradation isn't too extensive, a digital detector can restore the original signal. This restoration capability, despite signal impairment, is a significant benefit of digital systems. 

1. To synchronize the next steps with your practical experience, it's recommended to start anew: 

   - Detach all connections and power down the PicoScope. 

2. Set up the circuit: 

   - Link the AUDIO OSCILLATOR's sin(t) output both to the SEQUENCE G ENERATOR's input and the FREQUENCY COUNTER 

   - Connect the SEQUENCE GENERATOR's AUDIO OUTPUT to the BASEBAND CHANNELS FILTER input and Scope ChA.    

- Attach the BASEBAND CHANNELS FILTER's output to the ANALOG SIGNAL INPUT of the UTILITIES module and Scope ChB). 

3. Launch the PicoScope and configure it as follows: 

   - Adjust the timescale to 2ms/div. 

   - Activate ChB (set to Auto). 

   - Opt for Single Shot Triggering. 

   4. Unplug Scope ChB from the output of the BASEBAND CHANNELS FILTER. Instead, link the UTILITIES module's CLIPPER to Scope ChB. 

   - Note both the signal's delay and its inversion. 

   - It's evident that the digital signal is precisely retrieved, albeit inverted. 

5. Increasing the frequency will intensify the degradation of the digital signal as it moves through the system, specifically the BBLPF2. This intensification can eventually lead to inaccuracies in the revitalized digital signal. 

   - Monitor both the input and the retrieved digital signals as the frequency escalates. 

 

 

Table 5: Digital detector 

 

 

Conclusion  

I enjoyed the manipulation of signals throughout the lab.  The practice of in-class material is important as it helps the student gain a newfound appreciation for topics as well as a newfound understanding. I did not particularly enjoy the lengthy process of the lab as it became dreadful. Hopefully, future labs will be more fun and engaging from the student's perspective. I also was not too sure if my results were correct and could have used more answer validation for this instance. Overall, I learned more about signals, specifically about wavelength and time periods and how to read them.