ECEN 4872/5827 Lecture Notes


 Elwin Murphy
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1 ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals f Cmmn Mde ejectin ati (CM) 5. Fundamentals f Pwer Supply ejectin ati (PS) Analysis f Tlerances and Temperature Cefficient fr a Precisin Current eference Circuit Circuit: The gal is t have 1mA. f the pamp is ideal, and the BJT has very large current gain, v() v( ), and therefre Taking int accunt the pamp ffset vltage, the finite BJT current gain β, and the pamp input bias current B, we have (frm previus lecture): β s B (1) β 1 Neglecting B, we get: β s (2) β 1 Nte that if B were significant, the effect f B culd be canceled by adding a resistr (f the same resistance value, ) in series with the psitive pamp input.
2 Given the tlerances and temperature cefficients fr, OS, β, and, ur bjective is t find the tlerance and the temperature cefficient f. T slve this prblem, we linearize as a functin f, OS, β, and arund the nminal value : β s (3) β s β s Evaluating the abve partial derivatives using (2),, yields: β s 1 β (4) 2 2 (1 β ) Simplificatin and rearrangement f the abve equatin yields: 1 β β β s (5) Numerical example: β ±50% β ±0.1% s ±0.25% ±1% Appraches t Evaluating Tlerances There are tw general appraches fr evaluating individual tlerances Wrst Case Apprach Standard Deviatin Apprach The Wrst Case apprach, in general, is a very cnservative apprach where the maximum abslute values f the individual parameter tlerances are simply added: Tlerance ± ndividualtlerances ±1.85% (in this numerical example) (6) f the result f interest depends n a large number f individual parameters in a circuit, the wrstcase apprach leads t a very cnservative result. n such cases, a statistical
3 methd can be applied. Assuming that the individual parameter values can be cnsidered as independent randm variables with nrmal distributins, the standard deviatin f the result can be fund as 2 σ σ 1.2% (in this numerical example) (7) Ntes n the precisin current reference: The precisin current reference circuit is designed starting frm a precisin vltage reference, and using an pamp and a transistr in a negativefeedback cnfiguratin t set the reference current. The input ffset vltage OS f the pamp can have a significant effect n the tlerance f. n the precisin current reference design, the largest cntributr t the tlerance f is the resistr tlerance. n the numerical example, we assumed the resistr tlerance f ±1%, which can easily be accmplished using a discrete resistr. Fr resistrs that can be realized n an integrated circuit, the abslute tlerances are usually much wrse (e.g. ±20%), which can be a significant prblem in C design. Temperature Cefficient General Cmment: Unlike tlerances which are due t randm variatins f cmpnent parameters, temperature cefficients usually have knwn signs, making it pssible t cancel temperature cefficients. This cancellatin apprach is used t make precisin bandgap vltage references, which will be addressed later in class. Fractinal Temperature Cefficient f the reference current can be fund as: TCF ( ) (8) T and is expressed in % per degree C, r parts per millin (ppm) per degree C. Nte that TC F includes the term, which can be cmputed as in (3)(5), taking int accunt the temperature cefficients f the circuit parameters. The result is: where TC F 1 1 s ( ) TCF ( β ) TCF ( ) TCF ( ) β T s is the temperature drift f the ffset vltage, ±10µ/ C in the T numerical example (9)
4 β TC F ( β ) 1%/ C ppm/ C β T TC F ( ) 100 ppm/ C T TC F ( ) 1000 ppm/ C T Using (9) and the numerical values fr the precisin current reference circuit in Fig. 1, we get: 1 ppm ppm 10µ ppm TCF ( ) (10,000) 100 ± (10) 100 C C C 1.26 C Nte that the temperature cefficient f the current reference is affected mainly by the temperature cefficient f the resistr : 1000 ppm TCF ( ) TCF ( ) (11) C Cmmnmde ejectin ati (CM) The cmmn mde input is the vltage applied simultaneusly t bth the psitive and the negative inputs. t is accunted fr as fllws: Fr smallsignal inputs: v( ) v( ) Cmmn Mde input: v cm 2 Differential Mde input: v id v( ) v( ) v( ) v( ) A vid Acmvcm A ( ( ) ( )) Acm 2 The cmmn mde rejectin rati is defined as: The CM is usually expressed in db: CM A CM (12) Acm A [ db] 20lg (13) ACM The value f the CM can generally be fund in data sheets fr the particular pamp. t is f interest t relate the cncept f CM in terms f the input ffset vltage. Cnsider the circuit shwn belw:
5 Figure 2: Openlp pamp with CM input; ref v cm. deally, the CM is zer, and the utput is zer, but with a real pamp that has a finite CM this is nt the case. n the circuit f Fig. 2, the utput vltage can be set t zer, 0 by applying a differential vltage v id. n circuit frm, this lks as fllws: Figure 3: Openlp pamp with CM input and a differential input added t set the utput t zer. ref v cm n the circuit f Fig.3, we have Ntes: A v A v 0 (14) id cm cm 1 1 vcm id s A CM (15) A v cm id Equatin (15) shws that CM can be cmputed by finding hw the input ffset vltage depends n the input cmmnmde vltage, which in sme cases can be easier t find than by definitin (12). Based n (15), we can als cnclude that the effects f finite CM are similar t the effects f the input ffset vltage, except that s shuld be cnsidered a functin f the cmmnmde input vltage. A quick example: Suppse that CM 80dB (CM 10 4 ), and that the input cmmnmde vltage has an amplitude f CM 10. Frm (15), it fllws that the amplitude f the equivalent input ffset vltage prduced by the cmmnmde input as a 3 result f the finite CM is CM 10 1 m Pwer Supply ejectin atin (PS) The PS indicates hw much the supply vltage disturbances effect the uput f the pamp. Neglecting finite CM, CM CM A ( ( ) ( )) A ( DD ) A ( SS ) (16)
6 Here, A and A are the smallsignal gains frm the psitive supply rail DD t the utput, and frm the negative supply rail SS t the utput, respectively. Similar t CM, PS can be defined in terms f the gains r in terms f the dependence f the input ffset vltage n the supply vltages, PS 1 A OS A (17) PS 1 A OS A (18) n pamp data sheets, the tw PS values are usually expressed in db.
, which yields. where z1. and z2
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