3. Multivibrators

A multivibrator is any circuit that has two states and snaps between them. It comes in three flavors based on how many of those states are stable:

• Bistable (two stable states): the latch or flip-flop. Stays in either state until pushed. This is the classic memory element of Chapter 4.
• Monostable (one stable, one quasi-stable): the one-shot. Sits in the stable state until triggered, briefly visits the quasi-stable state for a fixed time $T$, then automatically returns.
• Astable (no stable states, both quasi-stable): the free-running oscillator. Cannot stop; oscillates between the two states forever.

All three are typically built from two cross-coupled amplifying elements (transistors, gates, or op-amps) plus timing components (Rs and Cs). The Schmitt trigger we just covered is a special case of the bistable.

3.1 The bistable revisited: latches and Schmitt triggers as bistables

We already have the SR latch and JK flip-flop from Chapter 4. The Schmitt trigger is also a bistable: it has two stable states (output high or low) and snaps between them when the input crosses a threshold. The threshold-based triggering distinguishes it from the SR-latch style.

Trigger circuits. Bistables in pulse circuits are usually triggered externally: you fire a brief input pulse to flip the state. Three common trigger arrangements:

• Symmetric triggering. Same trigger fires both directions. Each pulse toggles the state. This is the classic toggle flip-flop and is the fundamental building block of binary counters.
• Asymmetric triggering. Separate set and reset inputs.
• Steered triggering. A diode steering network ensures the trigger pulse goes only to the transistor that is currently on, turning it off (and letting the other one come on).

3.2 Monostable multivibrator: the one-shot

The monostable has one stable state. Without any input, the circuit sits in this state forever. Apply a brief trigger pulse, and the output flips to the quasi-stable state for a precisely controlled time $T$, then returns to stable.

Classic discrete-component monostable:

                  +VCC
                   |
            ┌──────*──────┐
           [Rc1]         [Rc2]
            |              |
           Vc1───┐        Vc2────── output (initially high)
            |    │         |
            |    C        [R]
            |    │         |
           T1───*         T2 (initially saturated, Vc2 ≈ 0)
            |    │         |
           GND   │        GND
                 │
                 └─── (R from Vcc charges this side of cap)

Idle: T2 is on (saturated), output (Vc2) is low. T1 is off, Vc1 is high. The cap C is charged to Vcc on T1's side.

Trigger: a brief negative pulse to T2's base turns it off, output goes high. Vc2 jumps up. The cap C, which was charged to Vcc, holds this voltage difference, so its left plate is now at Vcc but its right plate (T2's base) gets kicked down to about $-V_{CC}$, deeply turning off T2. T2 will stay off until C charges back up through R from Vcc. When the right side of C reaches 0.7 V, T2's base turns on, T2 saturates, output drops back low, and the circuit returns to the idle state.

The pulse width: the cap must charge from $-V_{CC}$ up to 0.7 V through resistor R, traveling toward $+V_{CC}$. Standard RC math:

$V_C(t) = V_{CC} - 2V_{CC} \cdot e^{-t/RC}$

Set $V_C = 0.7 \approx 0$ and solve:

$T \approx RC \ln 2 \approx 0.693 \, RC$

So the monostable pulse width is $T \approx 0.7 \, RC$, depending only on the timing components.

Retriggerable vs. non-retriggerable. An important distinction:

• Non-retriggerable. Once triggered, the monostable ignores further triggers until the current pulse expires. New triggers during the pulse have no effect.
• Retriggerable. Each new trigger restarts the timing. The output stays high as long as triggers keep coming faster than $T$. Used in motion-detector lights ("if motion detected, hold light on for 30 seconds; reset that 30-second timer on every new motion event").

Applications:

• Pulse stretching. A nanosecond-scale digital pulse becomes a microsecond pulse you can drive an LED with.
• Switch debouncing. On detected first edge, fire a 50 ms one-shot. Ignore further edges during the one-shot's pulse.
• Watchdog timers. A monostable that must be retriggered every $T$. If the CPU stops servicing the watchdog (because it has crashed or been compromised), the timer expires and triggers a reset. Critical safety feature in medical, automotive, aerospace, and industrial systems. The IEC 61508 standard for functional safety essentially mandates them.
• Frequency dividers with feedback.
• Glitch filters. Use a non-retriggerable monostable to ensure that two pulses in close succession look like one.

Hardware-security tie-in. Watchdog timers are a key target for fault-injection attacks: if you can glitch the chip such that a single watchdog reset doesn't fire (instead of crashing the whole chip), you might bypass authentication checks or roll the chip into a state where security state-machines lose synchronization. Conversely, watchdogs are a defense: a glitched chip whose execution flow is disturbed will likely fail to retrigger the watchdog, forcing a reset that wipes whatever attack progress was made.

3.3 Astable multivibrator: free-running oscillator

The astable has no stable state. It snaps back and forth between two quasi-stable states forever, generating a square wave at the output.

Classic two-transistor astable:

                    +VCC
                     |
            ┌────────*────────┐
            │                  │
          [Rc1]             [Rc2]
            │                  │
            *────── Vc1   Vc2 ──*    (outputs)
            │       │     │     │
            │       C1    C2    │
            │       │     │     │
            │       *──[R1] *──[R2]
            │       │     │     │
           T1       │     │    T2
            │       │     │     │
           GND     GND   GND   GND
                   
  C1 connects T1's collector to T2's base
  C2 connects T2's collector to T1's base
  R1, R2 charge the bases through Vcc

Symmetric ("rotational") operation: at any given moment, one transistor is on and the other is off. The cap on the "off" transistor's base is charging through R toward Vcc; the "on" transistor's collector is at saturation. When the charging cap reaches 0.7 V, the "off" transistor turns on, which pulls down the other side's collector via the cap (which was charged to roughly Vcc), kicking the other transistor's base far negative and turning it off. Now the roles reverse.

Each half-cycle is the time for the relevant cap to charge from $-V_{CC}$ up to 0.7 V through R from Vcc:

$T_{half} \approx 0.693 \, RC$

Total period: $T = 2 \times 0.693 \, RC = 1.39 \, RC$. Frequency:

$f = \frac{1}{1.39 \, RC} \approx \frac{0.72}{RC}$

For asymmetric components (different R or C on each side), each half-cycle's duration depends on its own RC, giving an asymmetric duty cycle, useful for generating non-50% pulses.

Real-world uses:

• Blinking LEDs (the canonical first-circuit project for new electronics students).
• Tone generators. Audible square waves at audio frequencies for buzzers, alarms, simple synthesizers.
• Clock pulses for digital circuits where high accuracy is not required.
• Charge pumps and voltage multipliers. An astable drives a diode-cap network that produces a higher voltage than the input.
• Inverters and switching power supplies. An astable drives a transformer or switching transistor to generate the AC waveform that gets rectified into a different DC voltage.

3.4 Voltage-controlled multivibrators

Replace one of the timing resistors with a voltage-controlled element: a transistor in linear mode acting as a variable resistor, or even a varactor diode acting as a variable capacitor. The output frequency now varies with control voltage. This is a voltage-controlled oscillator (VCO) in its simplest form.

Used in:

• PLL circuits for clock generation, frequency synthesis, and clock recovery (Chapter 7).
• FM modulators. The audio signal modulates the VCO's control voltage, producing FM directly.
• Frequency-modulated test signals.
• Theremin-style audio. Vary the control voltage with a hand near a sensor coil; pitch follows your hand.

Hardware-security tie-in. Ring oscillators (which are essentially astables made from an odd number of inverters in a loop) are widely used as physically unclonable functions (PUFs) and as true random number generator sources. The exact frequency of a ring oscillator depends on subtle manufacturing variations in transistor threshold voltages and propagation delays, so two nominally identical chips will have ring oscillators that run at slightly different frequencies. Cryptographic protocols can exploit these unclonable variations to generate device-unique secrets. Ring oscillators are also used as random-number sources because thermal noise causes their phase to drift: sample two oscillators at the same moment and the lower bits of their phase difference are random.