Module 4: Creating Linear Ramps – Time Base and Sweep Generators

1. Introduction to Time Base Generators
2. A Time Base Generator is a specialized electronic circuit designed to produce an output voltage or current that varies linearly with respect to time. The characteristic waveform produced by such a generator is commonly known as a sawtooth or ramp waveform. These signals are critically important in a variety of systems that rely on visual displays, most notably in Cathode Ray Oscilloscopes (CROs) and RADAR systems. In an oscilloscope, this linearly changing voltage is applied to the horizontal deflection plates to sweep the electron beam across the screen at a constant velocity, creating the “time” axis against which another signal can be measured. For this reason, time base generators are often referred to as Sweep Circuits.
3. The sawtooth waveform has two distinct phases, which correspond to the movement of the electron beam on a display:

• Sweep Time (TS): This is the portion of the waveform where the voltage increases linearly with time. During this phase, the electron beam is swept across the screen from one side to the other (e.g., left to right). This visible movement is known as the Trace.
• Restoration Time / Fly back Time / Retrace Time (Tr): This is the portion of the waveform where the voltage rapidly returns to its initial value. This action causes the electron beam to “fly back” to its starting point to begin the next trace. This Retrace is typically made to happen so quickly that it is invisible to the human eye.
• Time base generators are categorized based on the type of output they produce:
• Voltage Time Base Generators: These circuits produce an output voltage waveform that varies linearly with time.
• Current Time Base Generators: These circuits produce an output current waveform that varies linearly with time.
• In any practical sweep circuit, the generated ramp will deviate slightly from a perfectly straight line. This deviation from linearity is quantified by three types of errors:
• Slope or Sweep Speed Error (es): An ideal sweep has a constant slope. This error measures the difference in the slope of the ramp at the beginning of the sweep compared to the slope at the end. It quantifies how much the “speed” of the sweep changes over its duration.
• Displacement Error (ed): This error represents the maximum vertical difference between the actual, slightly curved sweep waveform and an ideal, perfectly linear ramp that passes through the same start and end points.
• Transmission Error (et): When a sweep signal is passed through a circuit (like a high-pass filter), its shape can be altered. This error measures the difference between the input and output sweep voltages at the end of the sweep time.
• For small deviations from linearity, these three errors are related by the following expression, indicating that the slope error is typically the most dominant: es = 2et = 8ed
• With these foundational concepts in place, we will now examine the practical circuits used to create these essential sweep waveforms.

1. Basic Time Base Generator Circuits
2. The simplest conceptual method for generating a ramp waveform is to utilize the charging behavior of a capacitor. However, as we will see, this basic approach is inherently non-linear and often insufficient for precision applications.
3. Simple Voltage Time Base Generator
4. This basic sweep circuit consists of a resistor (R) and a capacitor (C) connected in series to a supply voltage (VCC), with a Bipolar Junction Transistor (BJT) acting as a switch in parallel with the capacitor.
5. The operation is straightforward:
   1. A gating pulse is applied to the base of the BJT. When this pulse is high, it turns the transistor ON, driving it into saturation. The saturated transistor provides a very low-resistance path to ground, causing the capacitor C to discharge rapidly.
   2. When the gating pulse goes low, the transistor turns OFF. With the discharge path removed, the capacitor C begins to charge exponentially towards the supply voltage VCC through the resistor R. This charging portion of the cycle forms the sweep voltage.
6. The voltage across the capacitor during the charging phase is described by the standard exponential equation: V0 = VCC * [1 – exp(-t/RC)]
7. This equation reveals the fundamental limitation of this simple circuit: the charging curve is exponential, not linear. The output is only an approximation of a linear ramp. For the ramp to be reasonably linear, only a very small, initial portion of the exponential curve can be used, which severely limits the maximum amplitude of the sweep voltage.
8. Simple Current Time Base Generator
9. An alternative approach uses a transistor in a common-base configuration. The principle behind this circuit is that in a common-base setup, the collector current is very nearly equal to and varies linearly with the emitter current. By applying a ramp voltage to the transistor’s input, a linearly increasing emitter current is produced. This, in turn, generates a linearly increasing collector current, which can be passed through a load to create the desired sweep. The instantaneous load current is approximately iL ≈ (vi – VBE) / RE, showing a direct relationship with the input voltage vi.
10. Advanced Sweep Circuits for Improved Linearity
11. The inherent non-linearity of simple RC charging circuits is unacceptable for high-precision applications like laboratory oscilloscopes. To overcome this limitation, advanced circuits have been developed that employ feedback techniques to generate highly linear ramp waveforms. Two of the most important are the Bootstrap and Miller sweep generators.
12. Bootstrap Time Base Generator

• Core Concept: The key to generating a linear ramp is to charge the timing capacitor with a constant current. An exponential curve results from a charging current that decreases as the capacitor voltage rises. The technique of bootstrapping uses positive feedback to cleverly maintain a constant voltage drop across the charging resistor, which, by Ohm’s law (I = V/R), ensures a constant charging current.
• Construction: The Bootstrap circuit typically consists of a transistor Q1 acting as a switch, a second transistor Q2 configured as an emitter follower (a unity-gain buffer), a main timing capacitor (C1), a charging resistor (R), and a large “bootstrapping” capacitor (C2). The emitter follower Q2 is crucial, as its output voltage very closely follows its input voltage.
• Operation:
  1. Initially, a gating signal keeps the switch transistor Q1 ON, holding the timing capacitor C1 discharged. The large bootstrapping capacitor C2 is charged up to nearly the full supply voltage VCC through a diode.
  2. When the gating signal turns Q1 OFF, the sweep begins. The timing capacitor C1 starts to charge through resistor R.
  3. Here is the “bootstrap” action: As the voltage across C1 rises, this rising voltage is fed to the input (base) of the emitter follower Q2. The output of Q2 (at its emitter) rises in lockstep with the voltage on C1.
  4. This rising emitter voltage is connected to one side of the large capacitor C2. Because C2 is very large, it cannot discharge quickly and thus maintains a nearly constant voltage across itself.
  5. The other side of C2 is connected to the top of the charging resistor R. Because the voltage at the bottom of C2 is rising at the same rate as the voltage across C1, and the voltage across C2 is constant, the voltage at the top of C2 must also rise. This “pulls up” the voltage at the top of the charging resistor R, as if it were pulling itself up by its own bootstraps.
  6. The result is that the voltage difference across the charging resistor R is held nearly constant throughout the charging cycle. A constant voltage across R means a constant current flows through it, which in turn charges the timing capacitor C1 in a highly linear fashion.
• Advantage: The primary advantage of the Bootstrap generator is that the output ramp it produces is very linear. Furthermore, the amplitude of the ramp can reach nearly the full supply voltage level.
• Miller Sweep Generator
• Core Concept: The Miller Sweep Generator, also known as a Miller integrator, achieves linearity using a different principle: electronic integration combined with high-gain amplification. It is frequently used in horizontal deflection circuits.
• Construction: A typical Miller Sweep circuit is a multi-stage design. It often begins with an input stage controlled by a Schmitt Trigger, which operates a switch transistor (Q4). The core of the circuit is a high-gain inverting amplifier. The timing capacitor (C) is not connected from the input to ground, but rather as a feedback element between the input and the output of this high-gain amplifier. Emitter follower stages are often used at the input and output to act as buffers, preventing the amplifier from being loaded down and ensuring high input and low output impedance.
• Operation:
  1. The circuit is controlled by the output of a Schmitt Trigger. When the Schmitt Trigger’s output is high, the switch transistor Q4 is turned OFF.
  2. With Q4 OFF, the timing capacitor C begins to charge from a supply voltage (VBB) through a timing resistor (R).
  3. As a small voltage begins to build up at the input of the high-gain inverting amplifier, the amplifier produces a large, inverted (negative-going) output voltage.
  4. This large negative-going output is connected to the other side of the timing capacitor C. According to the Miller effect, this makes the capacitor C appear to the input as a much larger capacitor. The high gain of the amplifier ensures that the input voltage changes very little, forcing the charging current through R to remain almost perfectly constant.
  5. This constant current charging produces a highly linear negative-going ramp, or “rundown” sweep, at the amplifier’s output. At the end of the desired sweep period, the Schmitt Trigger’s output goes low, turning the switch transistor Q4 ON and rapidly discharging the capacitor to reset the circuit.
• The performance of a Miller sweep generator can be quantified by its slope speed error, es. This error is influenced by factors such as the amplifier’s gain (A), input resistance (Ri), and input capacitance (Ci). The relationship is given by the formula: es = (Vs/V) * (1 – A + R/Ri + C/Ci) Where Vs is the sweep amplitude and V is the supply voltage. This formula shows that a very high amplifier gain (A) is essential for minimizing the error and achieving excellent linearity.
• We have now seen how to generate precise linear waveforms. The next module will shift focus to specialized components that are not general-purpose transistors but are designed with unique characteristics that make them particularly well-suited for use in pulse and timing applications, beginning with the Unijunction Transistor.

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