Using RCtime to Measure Resistance

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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 buil-in 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(20.0E-3) ' 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(20.0E-3) ' 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 seady-sae 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 (1-1/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 full-scale 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 = 120.0E-6 ' Seconds Cons Capaciance As Single = 0.1E-6 ' 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 inpu-risae, hen measure how long he pin says ' a logic-high. 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, BX-01, BX-24 and BX-35 are rademarks of NeMedia, Inc. All oher rademarks are he propery of heir respecive owners A 5

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