MOSFET Internal Capacitances

Transcription

1 ead MOSFET Iteral aactace S&S (5ed): Sec. 4.8, 4.9, 6.4, 6.6 S&S (6ed): Sec. 9., 9.., 9.3., The curret-voltae relatoh we have dcued thu far for the MOSFET cature the ehavor at low ad oderate frequece. However, lar to the dode, at hh frequece, there are a uer of caactve effect that coe to lay. Thee effect ca e odeled y add varou caactor to the MOSFET lare ad all al odel we have ued thu far. For ow, let coder eerc al (could e lare or all). Frt, there oe erla etwee the ate ad S/D. Th erla caactace ve y W ox Wth a elf-aled roce, thee erla caactace ca e ade very all (.5... ). The reao that the ate telf erve a the a whe lat the S ad D reo. I addto, there a caactace etwee the ate ad the duced chael. The value of th ate caactace W ate ox How th ate caactve effect afet telf deed o the oerato ode of the trator. trode ate ate aturato 3 ate (due to taered chael) cutoff (there o chael) ate Fally, there alo the jucto caactace aocated wth the S-B ad D-B dode. Thee dode are revere aed. Fro our dcuo of dode, we ow: j ( V ) SB d j ( V ) DB EE ecture Note (Wter ) 8 -

2 The equato ae cature the caactve effect for a MOSFET for a eerc al, lare or all. I th coure, we are aly tereted the all al ehavor. For all al, the caactve effect afet theelve a all al caactor that are added to the all al odel. eeer, for all al, we wll aue the MOSFET aed aturato. The reult hh-frequecy all-al odel for the MOSFET aturato ow loo a follow: If S coected to B (whch tycally the cae th coure), th lfe to: 3 ate d d V V DB EE ecture Note (Wter ) 8 -

3 Hh Frequecy aly of the S lfer Matheatcal dervato We wll tudy a S alfer wth a caactve load added. Note that d ha ee lued toether wth. // r o U KV, K: V V out [ ] c a a [ ] [ ] ( ) ( ) c t low frequece ( ), the a correod to what we calculated efore (wthout clud caactve effect): Vout V Whe loo at the trafer fucto whe caactor are cluded, we otce that t ha oe (otve) zero ad two ole. Why are we tereted th trafer fucto? The reao that t ve u the frequecy reoe of the alfer. For ay alcato, t ortat to ow how ood the alfer wor er dfferet frequecy rae. EE ecture Note (Wter ) 8-3

4 ortat araeter of teret the 3-dB adwdth (ofte adwdth for hort). It dcate the frequecy where the (actual) a 3 db (factor of altude) elow the low frequecy a. H (db) 3 db 3dB (lo cale) We alo ow Bode lot, whch ve u a rahcal aroxato of the actual frequecy reoe u le eet. H (db) H GBW 3dB (lo cale) Doat ole aroxato for the S alfer Doat ole aroxato: If the ole are earated uffcetly far aart, the adwdth correod aroxate to the locato of the frt ole (udertad why). I that cae, we refer to the frt ole a the doat ole. << 3dB Sde ote: Ofte we are tereted the roduct of the low frequecy a ad the adwdth, rather tha a or adwdth dvdually. The reao that whe u the alfer feedac, we ca trade a off veru adwdth, ut the roduct rea the ae. ortat de etrc for alfer therefore th roduct, whch called the a-adwdth (GBW): GBW H 3dB O the Bode lot, we ca alo ee the a adwdth a the frequecy where the t -order art of the curve terect the db-ax (udertad why). EE ecture Note (Wter ) 8-4

5 et u ow o ac to the S alfer. We foud a ecod order trafer fucto. To fd the ole: a ue we have a doat ole: << a ( ) ( ) So the doat ole ve y the frt order ter of the deoator of the trafer fucto. Fro the doat ole aroxato earler, we alo ow th doat ole alo aroxately equal to the adwdth: 3dB The value of th doat ole deed o a lare uer of crcut eleet. To a oe tuto, let tudy the cae whe oly oe of the caactace o-zero. The actual te cotat (ee ae) the u of thee dvdual te cotat If oe of the doate, t allow u to ealy calculate the frt ole. I th cae, the doat ole aocated wth oe caactor ad the retace t ee. We wll revt th hortly. Oly : Oly : ( ) Oly : ( ) ( ) 8-5 EE ecture Note (Wter )

6 Doat ole aroxato eeral We ca eeralze the doat ole aroxato whe the trafer fucto of hher order (e.. for ore colex alfer cofurato that the S): deoator of the trafer fucto: whe oe ole doat:. The vere of the frt order coeffcet correod aroxately equal to the doat ole. The doat ole aroxately equal to the adwdth 3dB How to fd Gray ad Searle (969) have how that the frt order coeffcet (.e., the trafer fucto ae) ca e otaed a follow (th alway true, ut eecally ueful whe the doat ole aroxato hold ce t ay oeth aout the adwdth that cae): o The (..) are the caactace the crcut. o the retace that th caactace ee,.e. t the equvalet retace (le for Theve) etwee the teral of the caactace (whe all other caactor are tae out). EE ecture Note (Wter ) 8-6

7 Procedure: Ota the cotruto fro each caactace y ett all other caactace to zero (.e. they ecoe a oe), ett all deedet ource to zero, ad deter the retace ee y the caactace. Thee cotruto, called the oe-crcut te cotat, are the ued toether. ( ) 3 (Mller caactace) 3 (Gray & Searle) 3 db (doat ole aroxato) EE ecture Note (Wter ) 8-7

8 Mller effect The caactace the S alfer dlay what ow a the Mller effect. a exale, coder the follow crcut (alfer ha fte ut retace,.e. zero ut curret): _ V S - I V - V - I V V V V ( ) V I I ( ) V ( ) V I I V /( ) I V /( ) Th crcut ehave the ae (.e. ha the ae curret ad voltae) a: _ V V V S - I I Th called the Mller theore. Th hold eeral: V V V V V V V V Whe the a lare ( >> ): E.., f the edace are caactor, we ca trafor a crcut wth a float caactor to oe wth two rouded caactor. EE ecture Note (Wter ) 8-8

9 We oerved th Mller effect for the the S alfer. ( ) eq ) eq ( Due to the Mller effect, the aear o the ut ode a a uch larer caactace eq. alculat the aocated oe-loo te cotat: eq ( ) Ofte, the lat ter uch aller: eq ( ) Th a well-ow reult: a caactor etwee the ut ad outut ve re to a o-called Mller ole. I eece, the caactor ehave a f t were a uch larer caactor. EE ecture Note (Wter ) 8-9

10 De I alfer de, a tycal ecfcato a well-defed GBW (ofte axzed). Th eure that the alfer well-ehaved whe ued a feedac cofurato (reeer, t the GBW that cotat, deedet of the aout of feedac). To acheve th, the deer wll try to eure the reece of a doat ole. Th lfe the de, a we ca ue the doat ole aaly. 3dB o (Gray & Searle) (doat ole arox) 3dB o The eaet way to create a doat ole to ae oe of the oe-loo te cotat very lare. Th ca e doe y delerately lac a lare well-defed caactor the crcut. If oe were to rely ly o the teral caactace of the devce, ole would ot e welldefed (.e. roce deedet) ad tycally o oe ole would e doat. 3 db ax( ) o o (ae oe te cotat doat) (doat ole arox Gray&Searle) 3dB o Th deed reult a well-defed GBW: 3 db o H GBW H 3dB o EE ecture Note (Wter ) 8 -

11 Where to lace th exteral caactor? Tycal lace are () at the outut or () a a Mller caactace (ce a aller caactor wll do that cae, a we eeft fro the Mller effect). Ofte you wll fd that the crcut wll have oe lare caactor erted for th reao ( oetae or ult-tae alfer). B 3 db H 3dB ( ) B H GBW H 3dB GBW H 3 db B ( ) EE ecture Note (Wter ) 8 -