Electronics and Noise, Ch. 14 and 16, Senturia

• What determines the performance of a sensor?– Minimum Detectable Signal? (What does this mean?)– Precision?– Accuracy?– Frequency Response?– Dynamic Range? (What does this mean?)

Look at the ADXL 204

• Sensitivity– What is the significance?

• Noise Specs?– What is the signficance?

• Anything on accuracy or precision?– ?

Plan

• Start with elecronics – review op-amp circuits

• Talk about noise in general

• Do some examples using specs for particular op-amps.

• Another limitation, in addition to all the others, that comes from properties of the op-amp circuit:

• Slew-Rate:• The rate at which the output voltage can change• Typically measured in V/s (at the output)• It is another spec. for op-amps• Typically 0.5-1,000 V/s• Sometimes this needs to be large for driving

something like an electrostatic actuator.

Slew-Rate

Noise, Ch. 16, Senturia

• Noise often limits performance of MEMS sensors and other devices (oscillators, filters, for example).

• What we often think of as noise can be divided into 2 (or more) parts.

• 1. Interference.

• 2. Random noise.

• 3. Drift, aging effects… (random noise??)

Interference

• Definintion: Unwanted sensitivity to external or internal disturbances.– Electrical, thermal, mechanical, optical…

• Examples.– Electrical: Capacitive coupling to 60 Hz, radio waves,

driving voltage to output …– Mechanical: Sensitivity to vibration…– Optical: Sensitivity to ambient light.– Thermal: Sensitivity to temperature (very common!)– System design critical (Senturia has examples)– References: Keithley, Low-Level measurements +

others.

Random Noise

• Thermal noise.– Dissipative processes result in fluctuations.– Energy storage elements have a non-zero fluctuating

amount of energy stored.

• Shot noise.– Current consists of discrete particles.

• Flicker noise (1/f noise).– Mostly capture and release of carriers from traps in

electrical circuits. Many physical mechanisms, generally.

Thermal Noise

• Statistical mechanics -> average energy of a particle = 3/2 kBT. (1/2 KBT for each degree of freedom (x, y, z))

– Mass with 1 degree of freedom -> ½ kBT <-> inductor!

– Inductor has on average ½ kBT of energy.

– The capacitor is also an energy storage element with one degree of freedom. If connected to its environment with a resistor (or almost anything else) it has an average stored energy of ½ kBT! This does not depend on the size of the resistor or capacitor!

– Spring (capacitor) also has ½ kBT.

– This is characteristic of thermal noise.

4kT=4.1x10-21 at 300 K