Sample-and-hold capacitor voltage and advantages

A sample-and-hold (S/H) circuit samples an analog signal at a given instant and holds that value constant for a fixed time, so that an A/D converter can convert a steady input.

Circuit

           Switch S (MOSFET)
 Vin --[A1]--o/ o--+--[A2]--> Vout
                   |
                  === C (hold capacitor)
                   |
                  GND
      Logic control signal --> gate of S

• A1: input buffer (voltage follower) with very low output impedance.
• S: electronic switch controlled by the sample/hold logic signal.
• C: low-leakage hold capacitor (polystyrene/Teflon).
• A2: output buffer (voltage follower) with very high input impedance.

Sample (track) mode: S closed; C charges quickly through A1, and $V_{out}$ follows $V_{in}$. Hold mode: S open; C stores the voltage at the instant of opening.

How the voltage stays constant when the switch is open

The voltage across a capacitor changes only if current flows: $\frac{dV_C}{dt} = \frac{i}{C}$. When the switch is open, the circuit is designed so that $i \approx 0$:

1. Open switch: an OFF MOSFET has extremely high resistance, so no charge flows back to the input.
2. High-impedance output buffer: A2 (FET-input op-amp) draws only picoamperes, so the capacitor is not loaded.
3. Low-leakage capacitor: dielectric with very high insulation resistance.
4. Suitable C value: a larger C reduces droop rate.

Since $Q = CV$ is trapped on the capacitor, $V_C$ stays almost constant. A small fall called droop remains:

$$\frac{dV}{dt} = \frac{I_{leak}}{C}$$

Example: $I_{leak} = 1$ nA, $C = 1$ nF gives droop $= 1$ V/s, i.e. only 10 µV in a 10 µs conversion time.

Trade-off: large C means low droop but longer acquisition time in sample mode.

Advantages of digital control system over analog

• Flexible: control law changed by reprogramming, not rewiring.
• Accurate and drift-free: no change with temperature or ageing of components.
• Better noise immunity of digital signals.
• Complex/adaptive/nonlinear control is easy to implement in software.
• One computer serves many loops (time sharing), so cost per loop is low.
• Easy data storage, display, alarms and networking.
• Smaller, cheaper, more reliable hardware.