Using RCtime to Measure Resistance


 Paul Wright
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1 Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a builin ADC (Analog o Digial Converer) is perhaps he easies way o do his, i is also possible o use a digial I/O pin. This can be useful in cases where you don' have enough ADC channels, or if a paricular processor doesn' have ADC capabiliy. Procedure RCime BasicX provides a special procedure called RCime for his purpose. RCime measures he ime i akes for a pin o change sae o a defined value. By connecing a fixed capacior and a variable resisor in an RC circui, you can use an I/O pin o measure he value of he variable resisor, which migh be a device such as a poeniomeer or hermisor. There are wo common ways o wire an RCime sysem. The firs is o ie he variable resisor o ground. Figure 1 shows his configuraion. The advanage here is less chance of damage from saic elecriciy: Figure 1 Figure 2 The second configuraion is shown in Figure 2. Here we use he opposie connecion, where he capacior C is ied o ground and he variable resisor R V is ied o 5 vols: In boh circuis resisor R 1 is here o proec he BasicX chip's oupu driver from driving oo much curren when charging he capacior. To ake a sample, he capacior is firs discharged by aking he pin o he correc sae. In he case of Figure 1, he pin needs o be aken high (+5 V) o produce essenially 0 vols across he capacior, which causes i o discharge. In figure 2 he desired sae is low or ground. In eiher case, he capacior is discharged for a leas 4 ime consans, which is 4 R 1 C. Once his ime has elapsed, he capacior
2 should be sufficienly discharged. A his poin, he RCime procedure is called. RCime releases he capacior by making he pin a risae inpu. The procedure hen measures how long i akes o charge he capacior o he rip poin of he inpu pin. This ime inerval is a funcion of R V. If R 1 is negligible compared o R V, he ime inerval is proporional o R V. You may need o experimen wih differen values of capaciors o opimize he process. Example 1, using he circui from Figure 1: Dim TimeInerval As Single ' Discharge he capacior on pin 15. Call PuPin(15, bxoupuhigh) Call Delay(20.0E3) ' Wai abou 20 ms. ' Wai for a logic low on pin 15. Call RCime(15, 1, TimeInerval) Example 2, using he circui from Figure 2: Dim TimeInerval As Single ' Discharge he capacior on pin 15. Call PuPin(15, bxoupulow) Call Delay(20.0E3) ' Wai abou 20 ms. ' Wai for a logic high on pin 15. Call RCime(15, 0, TimeInerval) Poeniomeer example Symbols in his secion τ C I I 0 R 1 R V V 0 V c Time consan Capaciance Curren hrough po and capacior Iniial curren hrough componen Resisance of fixed resisor Resisance of po Time Iniial volage across componen Volage across capacior V R1 Volage across fixed resisor R 1 V RV V rip Volage across po Volage rip poin for he inpu pin 2
3 Circui behavior In his example, we'll use he same configuraion as Figure 1. A poeniomeer is used as he variable resisor R V and has a maximum resisance of 50 kω (see Figure 3 below): Figure 3 The following derivaion assumes R V is large compared o R 1. Tha is, R 1 / R V << 1. Discharging capacior  he firs sep is o discharge he capacior by raising he I/O pin. The pin needs o be held high long enough o allow V c o decay o a negligible value. For iniial condiions, assume he volage across he capacior has reached a seadysae 5 V. Also assume he pin acs like an ideal swich. A ime = 0, he pin is aken high, and he iniial curren hrough R 1 is I 0 = ( V 0 / R 1 ) = ( 5 V ) / ( 300 Ω ) = 16.7 ma The volage V C across he capacior a ime > 0 is I 0 R 1 V C = Here, he ime consan τ = ( 300 Ω ) ( 0.1 µf ) = 30.0 µs. A rule of humb is o allow he capacior o discharge for a leas 4 ime consans (120.0 µs, in his case), which means he volage will decay as follows: V 0 V R1 = e ( 4τ / τ ) = ( 5 V ) / e 4 = 91.6 mv 1.8 % of maximum Here we are neglecing he effec of R V on he capacior discharge. This is a reasonable approximaion only if R 1 is negligible compared o R V. 3
4 Measuring ime delay  now ha he capacior is discharged, we se he processor I/O pin o inpurisae, which essenially disconnecs R 1 from he circui. A new ime = 0, he iniial curren I 0 hrough capacior C and poeniomeer R V is A ime > 0, he curren I is I 0 = ( V 0 / R V ) = (5 V) / ( Ω) = 100 µa. I 0 I = The ime consan τ = R V C = ( Ω) (0.1 µf) = 5.00 ms. This represens is he ime i akes for he curren hrough he circui o drop by (11/e) or abou 63 % below is maximum value. The volage V RV across he po a ime > 0 is I 0 R V V RV = Now we need o know he rip poin V rip for he inpu pin, which is he volage a which he pin ransiions from logic high o logic low. This poin can vary somewha from pin o pin and needs o be deermined empirically. If we know V rip, he resisance of he po becomes R V = C ln ( V 0 / V rip ) For he Amel chip used in a BasicX sysem, V rip is in he neighborhood of 2.5 V and does no appear o be sensiive o emperaure changes. Assuming V 0 = 5 V and V rip = 2.5 V, he resisance is herefore R V = ( / C ) In oher words, for a consan capaciance, he resisance is linearly proporional o ime. In his example, he ime required o charge he capacior o V rip = 2.5 V is = ( 0.1 µf ) ( 50 kω ) / = 3.47 ms. Opimizaion  In his paricular applicaion, here is a radeoff beween accuracy and he ime required for measuremens. Higher accuracy requires a longer measuremen ime. RCime has a fullscale value of abou 71.1 ms and resoluion of abou µs (1 / of full scale), which needs o be aken ino accoun. 4
5 For a given resisance, once you've deermined he opimum rip ime, his is how o size he capacior: C = R V ln ( V 0 / V rip ) Low values of R V  he derivaions in his secion assume R 1 is negligible compared o R V. If his is no he case, he equaions are somewha more involved. In paricular, as he raio R 1 / R V increases, i becomes less valid o assume he capacior is fully discharged a he beginning of each measuremen cycle. In he limiing case where R V = 0, he capacior never discharges a all. Code example Sub GeResisance( _ ByRef Resisance As Single) ' Measures he resisance of a po aached o an I/O pin. End Sub Cons PoPin As Bye = 15 Cons DischargeTime As Single = 120.0E6 ' Seconds Cons Capaciance As Single = 0.1E6 ' Farads Cons TripVolage As Single = 2.5 ' Vols Cons IniialVolage As Single = 5.0 ' Vols Dim TimeInerval As Single, K As Single ' Raise he pin and discharge he capacior. Call PuPin(PoPin, bxoupuhigh) Call Delay(DischargeTime) ' Se he pin o inpurisae, hen measure how long he pin says ' a logichigh. Call RCime(PoPin, 1, TimeInerval) K = 1.0 / (Capaciance * Log(IniialVolage / TripVolage)) Resisance = TimeInerval * K This example is used wih he circui in Figure 3. Source code can be found in file Resisance.bas by NeMedia, Inc. All righs reserved. Basic Express, BasicX, BX01, BX24 and BX35 are rademarks of NeMedia, Inc. All oher rademarks are he propery of heir respecive owners A 5
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