Electronics Guide

The Schmitt Trigger

The Schmitt trigger is the quintessential hysteresis circuit, converting a slowly changing or noisy input into a clean digital output. Named after Otto Schmitt who invented it in 1934 while studying squid nerve fibers, this circuit uses positive feedback to create two distinct threshold voltages.

In an op-amp Schmitt trigger, the positive feedback network connects from the output to the non-inverting input. When the output is high, the positive feedback raises the effective threshold voltage that the input must exceed to cause a transition. When the output is low, the threshold is lowered. The difference between these thresholds is the hysteresis width, typically set by the ratio of resistors in the feedback network.

The hysteresis width should be chosen based on the expected noise amplitude. Setting the hysteresis slightly larger than the peak-to-peak noise ensures clean switching without false transitions. Too much hysteresis, however, reduces the circuit's sensitivity to legitimate signal changes.

Transistor-Based Hysteresis Circuits

Discrete transistor Schmitt triggers use the regenerative action of cross-coupled transistor pairs. In the classic two-transistor configuration, the emitters share a common resistor that provides the positive feedback mechanism. When one transistor turns on, it raises the emitter voltage, which tends to turn off the other transistor, reinforcing the original transition.

The threshold voltages depend on the transistor bias conditions and the shared emitter resistor value. Unlike op-amp versions where hysteresis can be set precisely with resistor ratios, discrete designs require careful analysis of transistor operating points. Temperature variations affect the thresholds, making discrete Schmitt triggers less precise but often faster than their op-amp counterparts.

Applications of Hysteresis

Hysteresis circuits find applications wherever noise immunity at switching thresholds is important:

• Signal Conditioning: Converting sine waves or noisy signals to clean square waves for digital processing
• Threshold Detection: Preventing oscillation in level-crossing detectors and comparators
• Switch Debouncing: Eliminating multiple transitions from mechanical switch contacts
• Thermostat Control: Providing temperature dead bands that prevent rapid cycling of heating or cooling systems
• Voltage Monitoring: Creating reliable power-on reset circuits with definite switching points

The SR Latch

The Set-Reset latch is the simplest memory element, constructed from two cross-coupled gates or transistors. Each gate's output connects to the other's input, creating a positive feedback loop that maintains whichever state was last established. The Set input forces the latch to its "1" state, while the Reset input forces it to "0".

The cross-coupled configuration ensures that once set, the latch remains set even after the Set input is removed. The positive feedback regeneratively maintains the state. This memory behavior persists as long as power is applied, making SR latches useful for storing status information, implementing control flip-flops, and building more complex sequential circuits.

Analog Latches and Sample-Hold Circuits

Positive feedback also enables analog memory functions. Regenerative comparators can capture and hold an analog decision, latching their output to indicate which input was larger at a specific moment. These circuits are essential in analog-to-digital converters where successive approximation requires holding comparison results.

Track-and-hold amplifiers use positive feedback during the hold phase to maintain output voltage with minimal droop. The regenerative action compensates for leakage currents that would otherwise discharge the hold capacitor, extending the valid hold time significantly.

Metastability Considerations

When input signals change near the switching threshold, bistable circuits can enter a metastable state where they hover between their two stable conditions. This metastability is an inherent consequence of positive feedback systems having an unstable equilibrium point between stable states.

Metastability resolves itself over time as noise or small asymmetries push the circuit toward one stable state. The resolution time follows an exponential distribution, meaning there is always some probability of remaining metastable for any given duration. System designers must account for this by allowing sufficient settling time or by using multiple synchronization stages.

Latching Comparators

A latching comparator samples its input difference at a clock edge and uses positive feedback to rapidly amplify this difference to a full logic swing. The regenerative action continues until the output saturates at one supply rail or the other. Once latched, the output holds its state regardless of subsequent input changes until the next clock edge.

The StrongARM latch is a popular regenerative comparator topology used extensively in analog-to-digital converters. It achieves high speed by using cross-coupled inverters that provide strong positive feedback once activated. During the reset phase, the cross-coupled nodes are precharged. When the clock activates the comparator, differential input transistors create a small imbalance that the regenerative pair amplifies to full swing in picoseconds.

Dynamic Comparators

Dynamic comparators operate in two phases: reset and evaluation. During reset, internal nodes are initialized to known states. During evaluation, positive feedback amplifies the input difference. This clocked operation eliminates static power consumption and provides inherent sample-and-hold functionality.

The double-tail comparator adds a second current source that activates during the regeneration phase, increasing positive feedback strength and accelerating the decision. This topology achieves excellent speed-power trade-offs in modern CMOS processes and is widely used in high-speed data converters.

Offset Compensation Techniques

Regenerative comparators amplify any input offset along with the signal, making offset cancellation essential for precision applications. Auto-zeroing techniques store the offset during a calibration phase and subtract it during normal operation. Chopper stabilization modulates the signal to a frequency where offset and low-frequency noise can be filtered out.

In multi-bit flash ADCs using many parallel comparators, trimming individual offsets becomes impractical. Instead, designers rely on redundancy and digital calibration, using extra comparator levels and post-processing to compensate for offset errors.

Avalanche Pulse Generators

Avalanche transistors can generate extremely fast pulses with rise times under one nanosecond. The circuit charges a capacitor through a resistor until the transistor's collector-base junction avalanches. The resulting discharge produces a sharp pulse with well-defined amplitude. After the discharge, the junction recovers, and the cycle repeats.

The avalanche process is inherently noisy, with timing jitter determined by the statistical nature of carrier multiplication. This jitter, while undesirable for precision timing applications, makes avalanche circuits excellent sources of random pulses for cryptographic applications and Monte Carlo simulations.

Selecting Avalanche Transistors

Not all transistors are suitable for avalanche operation. The avalanche voltage must be below the collector-emitter breakdown rating to prevent destructive failure. Additionally, the transistor must have adequate current gain during avalanche to sustain regeneration. Specialized avalanche transistors such as the 2N2369 and ZTX415 are characterized for this mode of operation.

Junction temperature significantly affects avalanche voltage, typically with a positive temperature coefficient. This characteristic can cause runaway if thermal management is inadequate. Proper heat sinking and current limiting are essential for reliable operation.

Applications of Avalanche Circuits

Avalanche circuits serve specialized needs where their unique characteristics provide advantages:

• Time-Domain Reflectometry: Generating picosecond pulses for measuring cable lengths and locating faults
• Laser Diode Drivers: Producing fast current pulses for pulsed laser applications
• Nuclear Instrumentation: Generating calibration pulses that mimic radiation detector signals
• Random Number Generation: Exploiting avalanche noise for true random bit sequences
• EMC Testing: Creating fast transients for immunity testing

Principles of Super-Regeneration

In a super-regenerative receiver, positive feedback is adjusted to just beyond the oscillation threshold. A quench oscillator periodically reduces the gain below the oscillation point, resetting the circuit. When the quench allows gain to increase, oscillations build up from noise. If an external signal is present at the resonant frequency, oscillations build up faster because they start from a larger initial amplitude.

The logarithmic relationship between input signal and build-up time provides automatic gain control, allowing the receiver to handle a wide dynamic range without overloading. A weak signal produces slower build-up, while a strong signal causes rapid build-up. The quench frequency determines both bandwidth and sensitivity, with lower quench rates providing higher gain but narrower bandwidth.

Design Considerations

The quench waveform shape significantly affects receiver performance. Linear or exponential quench signals provide different trade-offs between sensitivity and selectivity. The quench frequency must be at least twice the desired audio bandwidth to satisfy Nyquist criteria for the detected signal.

Super-regenerative receivers radiate energy at the tuned frequency due to the oscillation during build-up. This re-radiation can interfere with nearby receivers and may violate regulatory requirements. Shielding, antenna isolation, and low radiation designs help mitigate this issue.

Modern Applications

Despite being nearly a century old, super-regenerative receivers remain relevant for specific applications:

• Remote Keyless Entry: Simple, low-power receivers for automotive and building access
• Garage Door Openers: Cost-effective receivers for short-range control
• Tire Pressure Monitors: Ultra-low power receivers in battery-powered sensors
• Wake-Up Receivers: Always-on receivers that wake more sophisticated radios when a signal is detected
• ISM Band Communications: Simple receivers for 315 MHz and 433 MHz applications

Regenerative Amplification

A regenerative amplifier couples energy back into a tuned circuit in phase with the oscillation. As feedback increases, the circuit's effective resistance decreases, raising the Q factor. At the regeneration threshold, resistance becomes zero and the circuit oscillates. Operating just below this threshold achieves maximum Q enhancement while maintaining stability.

The enhanced Q follows the relationship Q_eff = Q_natural / (1 - loop gain), where loop gain approaches but never reaches unity. Practical Q multiplications of 10 to 100 times are achievable, transforming a modest coil with Q of 50 into an effective Q of several thousand.

Stability Considerations

Q-multiplied circuits are inherently sensitive to component variations and environmental changes. Any drift that increases loop gain above unity causes oscillation, while drift that decreases gain reduces the enhancement. Automatic gain control systems help maintain operation near the optimum point.

Temperature compensation is particularly important because both active device gain and resonator components drift with temperature. Crystal-stabilized reference oscillators can provide error signals for feedback systems that adjust the regeneration level.

Applications

Q-multiplication finds use wherever high selectivity is needed without expensive high-Q components:

• Radio Receivers: Enhancing selectivity of simple tuned circuits
• Spectrum Analyzers: Creating narrow bandwidth filters for frequency analysis
• Instrumentation: Building high-Q resonators for precision measurements
• Wireless Power Transfer: Compensating for losses in coupled resonator systems

Creating Negative Resistance

Active circuits can synthesize negative resistance through positive feedback. A common approach uses an operational amplifier with its non-inverting input connected to a current-sensing resistor. As current flows through the circuit, the op-amp generates a voltage that opposes the applied voltage, making the circuit appear to have negative resistance at its terminals.

The magnitude of synthesized negative resistance can be controlled by adjusting feedback network values. This allows designing circuits with precisely specified negative resistance values, something not possible with naturally occurring negative resistance devices.

Negative Impedance Converters

A negative impedance converter (NIC) transforms a positive impedance into its negative equivalent. Using an operational amplifier with carefully arranged feedback, any impedance connected to the NIC input appears as a negative impedance of the same magnitude at the output. This technique enables simulating inductors with capacitors, creating non-Foster circuit elements, and canceling parasitic impedances.

NICs find applications in antenna matching where they can cancel the reactive component of an antenna's impedance, providing broadband matching that passive networks cannot achieve. However, stability analysis becomes complex because negative resistance can cause oscillation if not properly controlled.

Loss Cancellation

Negative resistance can cancel the positive resistance representing losses in a resonant circuit. Adding a negative resistance element in parallel with a lossy inductor effectively removes the loss, raising the Q factor. This technique underlies Q-multiplication and is used in precision oscillators to minimize phase noise.

Complete loss cancellation results in oscillation, so practical applications maintain a small net positive resistance for stability. The ability to tune the negative resistance provides a convenient way to optimize circuit performance or compensate for component aging.

Tunnel Diode Characteristics

The tunnel diode's current-voltage characteristic shows a region where current decreases as voltage increases, creating negative differential resistance. This region occurs at low voltages, typically below 0.5V, making tunnel diodes compatible with low-voltage circuits. The negative resistance region is bounded by a peak current at lower voltage and a valley current at higher voltage.

Tunnel diode switching times can be in the picosecond range because current flow involves quantum tunneling rather than minority carrier diffusion. This makes tunnel diodes among the fastest semiconductor devices available, though their small current capacity limits applications to low-power circuits.

Amplifier Design

A tunnel diode amplifier uses the negative resistance region to provide gain. The diode is biased in the negative resistance region where small signal variations cause amplified responses. The amplifier's gain depends on the ratio of load resistance to the magnitude of negative resistance.

Stability requires careful attention to bias and termination. If the total resistance seen by the diode becomes negative at any frequency, oscillation results. Resistive loading, frequency-selective networks, and careful layout minimize parasitic resonances that could cause spurious oscillations.

Applications and Limitations

Tunnel diode amplifiers serve niche applications where their unique properties provide advantages:

• Low-Noise Preamplifiers: The tunnel diode's quantum noise mechanism can provide lower noise than conventional amplifiers at microwave frequencies
• High-Speed Triggers: Picosecond switching enables ultra-fast pulse circuits
• Frequency Multipliers: The nonlinear characteristic generates harmonics efficiently
• Microwave Oscillators: Simple oscillators reaching tens of gigahertz

Manufacturing challenges and limited availability have restricted tunnel diode adoption. Modern alternatives including resonant tunneling diodes (RTDs) offer similar characteristics with better manufacturability, extending the frequency range into the terahertz region.

Stability Management

• Define Operating Boundaries: Clearly establish the conditions under which the circuit should oscillate, latch, or amplify
• Account for Tolerances: Component variations can push marginally stable circuits into oscillation
• Consider Temperature Effects: Gain changes with temperature can alter positive feedback levels
• Analyze All Frequencies: Ensure stability at frequencies outside the intended operating range
• Include Start-Up Provisions: Circuits that should oscillate must reliably start under all conditions

Noise Considerations

• Noise Amplification: Positive feedback amplifies noise along with signal, potentially limiting dynamic range
• Jitter in Timing Circuits: Regenerative switching times depend on noise, causing timing uncertainty
• Bandwidth Selection: Limiting bandwidth reduces integrated noise without sacrificing necessary performance

Testing and Verification

• Measure Hysteresis: Verify threshold voltages match design intent
• Check Over Voltage and Temperature: Ensure proper operation across the full operating range
• Probe for Oscillation: Look for unwanted oscillation at frequencies above the intended bandwidth
• Verify Margins: Confirm adequate margin exists between operating point and instability