BJT Mismatch parameters

27 September 2021 0 Comments



Mismatch parameters

Bipolar mismatch can happen due to 3 parameters:
  1. IS Mismatch
  2. β Mismatch
  3. RE Mismatch

There are 2 methods to extract the Bipolar Mismatch parameters. Let us analyze both methods to determine which method represents all 3 mismatch sources adequately.

Measurement Method 1


In this method the setup is made as shown above. Here the emitter currents are the same and the difference in the Vbe’s can be directly measured in the 2 side by side devices.
Wehave:
ΔVBE=VBE1VBE2


IS Mismatch only

If the BJT has IS mismatch only:
ΔVBE=VBE1VBE2=nVTlnIEIS2IEIS1=nVTlnIS2IS1

ΔVBEnVTΔISIS


Beta mismatch Only

If BJT has β mismatch only:
ΔVBE=VBE1VBE2=nVTlnIC1IC2

IC1=β11+β1IE

IC2=β21+β2IE

ΔVBE=VBE1VBE2=nVTln(β1(1+β2)β2(1+β1))

Set:
β1=β+Δβ2

β2=βΔβ2

ΔVBE=nVTln((β+Δβ2)(1+βΔβ2)(βΔβ2)(1+β+Δβ2))

ΔVBE=nVTln(1+Δββ(1+β)Δβ2(Δβ2)2)

ΔVBE=nVTΔββ(1+β)


Re Mismatch only

If BJT has RE mismatch only:
ΔVBE=VBE1VBE2=IE(RE1RE2)


Measurement Method 2


In this method the setup is made as shown above. Here the Vbe’s of both side by side transistors are forced equal and their collector currents can be measured.
ΔVBE=VTlnIC2IC1


IS Mismatch only

IC1=IS1exp(VBEnVT)
IC2=IS2exp(VBEnVT)

IC2IC1=IS2IS1

ΔVBE=VTlnIS2IS1


Beta mismatch Only

Since IS will be same and VBE is the same the measured IC will be the same so we do not detect any mismatch due to Beta mismatch.

Re Mismatch only

ΔVBE=VTlnIC2IC1
IC1=αIE1

IC2=αIE2

IC2IC1=IE2IE1

ΔVBE=VTlnIE2IE1

IE1RE1+VBE1=IE2RE2+VBE2

IE1=IT+ΔI2

IE2=ITΔI2

RE1=RE+ΔRE2

RE2=REΔRE2

IE1RE1IE2RE2=ITΔRE+REΔI

ITΔRE+REΔI=nVTlnIE2IE1

ITΔRE+REΔI=nVTln(1ΔIIE1)

ITΔRE+REΔInVTΔIIE1=nVTIE1IE2IE1=nVT(1IE2IE1)

Setting ΔI=IE1IE1IE2IE1IT(1IE2IE1)
ITΔRE+REIT(1IE2IE1)=nVT(1IE2IE1)

Solving for IE2IE1:
IE2IE1=1+ITΔREnVT+ITRE

ΔVBE=VTlnIE2IE1=VTln(1+ITΔREnVT+ITRE)VTITΔREnVT+ITRE


Comparison of the Methods

Mismatch Factor Method 1 Method 2Comment
ISΔVBE=nVTlnIS2IS1ΔVBE=VTlnIS2IS1Both methods represent this mismatch
βΔVBE=nVTΔββ(1+β)ΔVBE=0Method 2 cannot measure the mismatch due to Beta
REΔVBE=IE(RE1RE2)ΔVBEVTITΔREnVT+ITREMethod 1 gives a better reading

This Method 1 should be the method used to measire the mismatch parameter for a BJT since it includes effects from all 3 mismatch parameters.
NOTE: Mismatch will increase with temperature due to VT dependance