Understanding Sensors, Filters, and Data Conversion

Resolution and Sensitivity

Resolution = MaxV / (2^bit - 1).

Linear Potentiometer

Total Resistance = 800 Ohms, E = 2V, L = 10 cm.

Sensitivity = V/L. Max/Min Z.

Z_out = || 80{10 - |x|}.

Z_min = 0 Ohms.

Z_max = 400 || 400 = 200 Ohms.

Unknown input impedance = voltage follower.

Gauge Factor

20mm wire strain gauge resistance = 150 Ohms. Under force tension, R changes by 5, and L changes to 0.08.

Load Cell

Load Cell Sensitivity / Minimum Value of N.

LC makes a change in V from 0 to 2V. V varies linearly.

LCS = 2V / 10N = 0.2 V/N.

Minimum Value of N = 10N / 0.1N = 100, 2⁶.

Filters

IIR Filter Identification

Unbounded, non-causal.

IIR/Unbounded. y[n-1] = 200x[n] + 300x[n-1] - 500x[n-2]. Non-causal.

Digital-to-Analog Conversion

N-bit R-2R Ladder

V = 0/6.4. n = 5.

Maximum V_out = ?

Output V when input = B10010?

Temperature Sensing

Temperature Sensor (18-bit)

Equation to express x and y: E = 2V, L = 10cm, TR = 800 Ohms. 200R in series.

y = (80x / 1000) * 2V -> y = 160/1000 * x -> y = 0.16x -> x = y / 0.16 = 6.25y.

Working on temperature sensor. Change in output voltage as temperature increases. Range 20-50. Resolution of only 0.1°C. How many bits, require 0.01°C?

0. 1 = 30 / (2ⁿ - 1) -> 2ⁿ - 1 = 300. At least 9 bits.

1. 01 = 30 / 2ⁿ - 1 = 3000, At least N = 12 for 0.01.

Capacitive Sensors

Whenever capacitor plates move closer, capacitance increases, and positive charges leave the lower capacitor.

In the capacitive sensor, the top plate moves sideways. This displacement is measured by observing the change in capacitance. Larger sensitivity = side-a is shorter than side-b.

If the dielectric constant between two plates of a capacitor increases, it holds more charge.

Digital Filters

T = smoothing filter given by y[n] = ax[n] + (1-a)y[n-1], 0 < a. The effects of an individual sample never die out.

F = N > 5 is a high-pass filter, y[n] = Σ_i=0^n-1 (1/N) * x[n-i].

F = The cutoff frequency of a digital filter does not depend on the sampling rate.

Circuit Sensitivity

(a) You are using a voltmeter to observe the voltage across the current source. (b) You are using an ammeter to observe the current leaving the voltage source. Find the sensitivity for these two circuits with proper units.

(a) V = 6(2+R), S = dV/dR = 6 V/Ohms.

(b) 5 = RI, dI/dR = -5/R² A/Ohms.

Sensor Range

Range of the sensor you are trying to measure, V_ss.

Convolution

Convolution x = [1, -1, 0, 2], h = [0, 2, -1] -> x*h = [0, 2, -3, 1, 4, -2].

R-2R DAC

General structure of an n-bit R-2R DAC, input pins are 0 or 3.3V, n=7. Output voltage when input B1100100 -> (1/2 + 1/4 + 1/32) * 3.3 = 2.58V.