Building the humidity sensor circuit

With the wife out-of-town on business, I've been able to spend some time experimenting with the circuitry I'll need to construct the capacitive humidity sensor.

Previously, I had constructed a prototype based upon schematics I found on the Internet for an Arduino weather station, which used the same HCH-1000 sensor.  I tested the circuit in KTechlab and it seemed to simulate very well.  However, in my rush to produce the circuit, I made some mistakes while adapting it to a much smaller SMD populated circuit, and ended up burning my finger quite badly during testing.  It's a long story, but, needless to say, I've relearned my lesson.  Whenever you are building a circuit, it's always better to have a full understanding of what's happening within that circuit rather than just assembling it from a schematic. 

With this in mind, I spent much of yesterday re-immersing myself in the properties of our good friend the 555 timing circuit.  About two or three years ago, I had used the 555 to build a heterodyning ultrasonic bat detector, but I haven't worked much with them since and forgot most of the basics.  Specifically, I'm referring to astable operations in which the 555 is configured with two resistors and a capacitor to create a multivibrator (i.e. oscillator).  Adjusting either of the two resistors or the capacitor will change the nature of the oscillation frequency. There are a few useful equations which can be used to determine the outcomes of different combinations of resistors and capacitors, which I have captured in an annotated Python script called T555.py. 

# -*- coding: utf-8 -*-
"""
Created on Fri Aug  9 12:20:02 2013

@author: dan
"""
# capacitance is in Farads and resistance is Ohms

#Calculates the charging time of the capacitor (C) for resistor a (Ra) and resistor b (Rb). 
def chT(Ra,Rb,C):
    cT = 0.693*(Ra+Rb)*C
    return cT

#Calculates the capacitor discharge time   
def dT(Rb,C):
    diT = 0.693*Rb*C
    return diT

#Calculates the time for both capacitor charge and discharge
def TT(Ra,Rb,C):
    cT = chT(Ra,Rb,C)
    diT = dT(Rb,C)
    T = cT + diT
    return T

# Calculates the oscillation frequency output produced by Ra, Rb, and C  
def Freq(Ra,Rb,C):
    O = 1.44/((Ra+(2*Rb))*C)
    return O

#Calculates the duty cycle produced by the resistors and capacitors, which is a proportion comparing the charge time to the discharge time. 
def dC(Ra,Rb):
    D = float(Rb)/(Ra+(2*Rb))
    return D

#Calculates the combined value of both resistors based upon the known oscillation and capacitance
def AB2(O,C):
    ab2 = 1.44/(C*O)
    return ab2

# Calculates the individual values of Ra and Rb based upon the known duty cycle, oscillation, and capacitance
def AB(D,O,C):
    ab2 = 1.44/(C*O)
    Rb = ab2*D
    Ra = ab2-(Rb*2)
    print "Resistor A: " + str(format(int(Ra),","))
    print "Resistor B: " + str(format(int(Rb),","))

# Reports calculations for charge time, discharge time, total time, frequency, and duty cycle. 
def rt(Ra,Rb,C):
    cT = chT(Ra,Rb,C)
    diT = dT(Rb,C)
    T = cT + diT
    O = 1.44/((Ra+(2*Rb))*C)
    D = float(Rb)/(Ra+(2*Rb))
    print "Charge time (seconds): " + str(cT)
    print "Discharge time (seconds): " + str(diT)
    print "Total time (seconds): " + str(T)
    print "Frequency (Cycles per Second): " + str(O)
    print "Duty cycle: " + str(D)



In addition to the above script, I also wrote a script called Farads.py that gives you easy conversions between commonly used Farad units.  I did this because I loath making these conversions.

# -*- coding: utf-8 -*-
"""
Created on Fri Aug  9 13:57:53 2013

@author: dan
"""

def cF(number,faradunit):
    if faradunit == "F":
        F = number
    elif faradunit == "mF":
        F = float(number)/1000
    elif faradunit == "uF":
        F = float(number)/1000000
    elif faradunit == "nF":
        F = float(number)/1000000000
    elif faradunit == "pF":
        F = float(number)/1000000000000
    else:
        print "faradunit must be F, mF, uF, nF, or pF"
   
    mF = F*1000
    uF = F*1000000
    nF = F*1000000000
    pF = F*1000000000000
   
    print "farads:      " + str(format(F,",")) + " F"
    print "millifarads: " + str(format(mF,",")) + " mF"
    print "microfarads: " + str(format(uF,",")) + " uF"
    print "nanofarads:  " + str(format(nF,",")) + " nF"
    print "picofarads:  " + str(format(pF,",")) + " pF"



Once these scripts were placed in my "site-packages" folder, I was able to use the following workflow:

At 55% relative humidity, the HCH-1000 has a normal capacitance of 330 pico Farads.  Let's say that I want to measure the capacitance of the HCH-1000 500 times per second (I still haven't figured out what the ideal measurement frequency would be for Arduino, so this is just a place holder) and a duty cycle of 0.50.  In python I would do the following:

>>> import Farads as F
>>> F.cF(330,"pF")

the program would then return:

farads:      3.3e-10 F
millifarads: 3.3e-07 mF
microfarads: 0.00033 uF
nanofarads:  0.33 nF
picofarads:  330.0 pF

next, I type:

>>> import T555 as T
>>> T.AB(0.49,500,3.3e-10)

note that I use 0.49 and not 0.50.  This is because  0.50 is and ideal number that produces an Ra value of 0.

The results are:

Resistor A: 174,545
Resistor B: 4,276,363

Now, using a table for commonly used resistor values, I see that 180,000 and 4,300,000 Ohm resistors are likely to exist.  It may be likely that these slight changes to the resistance values will have little effect, but I can test is to be sure:

>>> T.rt(180000,4300000,3.3e-10)

Which returns:

Charge time (seconds): 0.0010245312
Discharge time (seconds): 0.000983367
Total time (seconds): 0.0020078982
Frequency (Cycles per Second): 496.997307931
Duty cycle: 0.489749430524

This close enough.  I'll write more later, but I wanted to note one more thing.  Yesterday, I checked the status of a container of sugar water I had placed in the beehive the day before to feed the bees.  It was completely empty!  They had managed to drink more than a gallon of 1:1 sugar/water solution in less than 24 hours.  In response, I created a new batch of 2:1 sugar/water solution and placed it in the hive yesterday evening.  I'll be interested in checking again today to see how far they've gotten with that batch.