Square and Pulse Generators

Comprehensive Technical Notes: Square and Pulse Generators

source: foysal sir video

This document provides a highly detailed, non-summarized technical analysis of the design, mathematics, and block-level architecture of laboratory-grade Square and Pulse Generators, based on the lecture material from VID-20260429-WA0011.mp4.

1. Introduction & Fundamental Applications

Square and pulse generators are indispensable signal sources used in electronic testing and measurement. They serve as primary stimulus instruments, typically operated in combination with a Cathode Ray Oscilloscope (CRO) to analyze the behavior of networks, active components, and systems.

A. Core Measurement Roles

• Quantitative & Qualitative Evaluation: These generators provide both types of information for a System Under Test (SUT):

  • Qualitative Information: Observed by sending a fast-rising pulse through a system and watching the distortion on a CRO. This reveals characteristics like phase distortion, ringing, overshoot, and bandwidth limitations.

  • Quantitative Information: Obtained by measuring specific output parameters such as rise time ($t_r$), settling time, propagation delay, and voltage levels.

• Transient Response Testing: They are heavily utilized to test the transient response of amplifiers and linear networks. Applying a high-speed step input (or a pulse approximating a step) allows engineers to analyze the stability, high-frequency performance, and damping factor of an amplifier without sweeping across a massive range of individual sine wave frequencies.

2. The Key Distinction: Duty Cycle

While both square and pulse waves consist of rapid transitions between two discrete voltage levels (High and Low), they are differentiated by their duty cycle.

      SQUARE WAVE (50% Duty Cycle)                 PULSE WAVE (Variable Duty Cycle, e.g., 25%)
        ┌──────┐      ┌──────┐                       ┌──┐          ┌──┐
        │      │      │      │                       │  │          │  │
   ─────┘      └──────┘      └─────             ─────┘  └──────────┘  └─────
        |<─ToN─>|<─Toff─>|                           |ToN─>|<─ Toff ──>|
        |<─────── T ────>|                           |<─────── T ─────>|

A. Mathematical Formulations

The Duty Cycle ($D$) is defined as the ratio of the pulse width (active duration) to the total period of the waveform.

$\text{Duty Cycle}=\frac{\text{Pulse Width}}{\text{Pulse Period}}=\frac{T_{\text{ON}}}{T}$

Where:

• $T_{\text{ON}}$ is the duration for which the pulse remains at its active (High) voltage level.

• $T_{\text{OFF}}$ is the duration for which the pulse remains at its inactive (Low) voltage level.

• $T$ is the total period of the wave, where:

$T=T_{\text{ON}}+T_{\text{OFF}}$

Expressing this as a percentage:

$\text{Duty Cycle (\%)}=\left(\frac{T_{\text{ON}}}{T_{\text{ON}}+T_{\text{OFF}}}\right)\times 100\%$

B. Parameters of Comparison

1. Square Wave Generator:

   • Features a strict $50\%$ duty cycle.

   • The active high time is exactly equal to the inactive low time:

$T_{\text{ON}}=T_{\text{OFF}}=\frac{T}{2}$

2. Pulse Generator:

   • Features a variable duty cycle that can typically be adjusted dynamically.

   • On laboratory-grade units, the duty cycle can be varied continuously from $25\%$ to $75\%$ (and in some high-end generators, even wider ranges like $1\%$ to $99\%$).

   • Allows independent control over pulse width ($T_{\text{ON}}$) and repetition frequency ($f=\frac{1}{T}$).

3. Block Diagram & Architectural Analysis

To generate highly stable triangular, square, and pulse waveforms with variable frequency and symmetry, laboratory instruments use an integrator-bistable feedback loop. Below is the detailed block-level architecture of a typical pulse generator.

                         [ SYMMETRY CONTROL ]
                                  │
                       ┌──────────┴──────────┐
                       ▼                     ▼
             ┌──────────────────┐  ┌──────────────────┐
             │  Upper Current   │  │  Lower Current   │
             │      Source      │  │      Source      │
             └─────────┬────────┘  └─────────┬────────┘
                       │                     │
                       ▼                     ▼
  [ FREQ. HZ ] ──> ┌──────────────────────────────┐
  (Freq. Control)  │       Switching Circuit      │
                   └──────────────┬───────────────┘
                                  │
                                  ▼
                         ┌────────────────┐
                         │ Ramp Capacitor │
                         └────────┬───────┘
                                  │
                                  ▼
                         ┌────────────────┐
                         │Buffer Amp. (A) │
                         └────────┬───────┘
                                  │
                                  ├────────────────────────┐
                                  ▼                        ▼
                         ┌────────────────┐      ┌──────────────────┐
     [ SYNC. INPUT ] ──> │Schmitt Trigger │ ──>  │  Trigger Output  │ ──> [ TRIGGER OUT ]
                         └────────┬───────┘      │     Circuit      │     (With Polarity Control)
                                  │              └──────────────────┘
                                  ├────────────────────────┐
                                  ▼                        ▼
                         ┌────────────────┐      ┌──────────────────┐
                         │Output Amplifier│      │50 Ω Output Amp.  │
                         │ (600 Ω Output) │      │(Step Attenuator) │
                         └────────┬───────┘      └─────────┬────────┘
                                  ▼                        ▼
                           [ 600 Ω OUTPUT ]          [ 50 Ω OUTPUT ]
                            (Rise/Fall ~70ns)        (Rise/Fall ~30ns)

A. Functional Walkthrough of the Circuit Blocks

1. Frequency Control (Freq. Hz):

   • Governs the rate at which the ramp capacitor charges and discharges.

   • Typically adjustable across seven decade steps spanning from $1\text{ Hz}$ to $10\text{ MHz}$, accompanied by a linearly calibrated dial for continuous vernier frequency adjustments.

2. Symmetry Control:

   • Adjusts the ratio between the current supplied by the Upper Current Source ($I_{\text{up}}$) and the Lower Current Source ($I_{\text{low}}$).

   • If $I_{\text{up}}=I_{\text{low}}$, the ramp capacitor charges and discharges at identical rates, producing a symmetrical triangular wave and a $50\%$ duty cycle square wave.

   • Adjusting symmetry varies the relative charge/discharge rates, creating an asymmetric ramp and a variable-width pulse.

3. Upper & Lower Current Sources:

   • Deliver constant, highly linear currents to the charging node. Using constant current sources ensures that the voltage across the ramp capacitor rises and falls in a perfectly linear fashion ($V_c(t)=\frac{I\cdot t}{C}$), rather than exponentially.

4. Switching Circuit:

   • An electronic switch controlled by the state of the Schmitt Trigger. It routes either the upper current source to charge the ramp capacitor upward or the lower current source to discharge it downward.

5. Ramp Capacitor & Buffer Amplifier ($A$):

   • The capacitor serves as the timing element.

   • The high input impedance buffer amplifier ($A$) prevents loading on the timing capacitor, ensuring the linear ramp profile is preserved as it is passed to the Schmitt Trigger.

6. Schmitt Trigger:

   • A bistable circuit with upper and lower voltage thresholds ($V_{UT}$ and $V_{LT}$).

   • When the charging capacitor ramp reaches $V_{UT}$, the Schmitt Trigger fires and changes its output state. This commands the switching circuit to stop charging and begin discharging via the lower current source.

   • When the discharging ramp falls to $V_{LT}$, the Schmitt Trigger flips back, restarting the charging cycle.

   • This self-oscillating loop forms the foundation of the generator.

7. Sync. Circuit & Input:

   • Allows the generator’s internal frequency to be locked (synchronized) to an external reference clock or system signal.

8. Trigger Output Circuit:

   • Leverages the fast transitions of the Schmitt Trigger to output a dedicated auxiliary synchronization pulse (Trigger Output) for triggering external devices like CROs.

   • Features a Trigger Polarity toggle to output either positive-going or negative-going trigger spikes.

9. Dual Output Stages:

   • $600\Omega$ Output Stage: Designed for general-purpose high-impedance applications. It features an adjustable Output Amplifier with a Vernier and Amplitude control. Typical rise and fall transitions are around $70\text{ ns}$.

   • $50\Omega$ Output Stage: Engineered for high-frequency RF and digital distribution. It includes a high-speed output driver and a Step Attenuator to make precise, discrete power/voltage adjustments. It delivers rapid transitions with a rise and fall time of approximately $30\text{ ns}$ to minimize high-frequency distortion and edge jitter.