BJT Mismatch parameters

27 September 2021 Link

Mismatch parameters

Bipolar mismatch can happen due to 3 parameters:
  1. $I_S$ Mismatch
  2. $β$ Mismatch
  3. $R_E$ 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.

$I_S$ Mismatch only

If the BJT has $I_S$ mismatch only:


Beta mismatch Only

If BJT has $β$ mismatch only:









Re Mismatch only

If BJT has $R_E$ mismatch only:

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.

$I_S$ Mismatch only


$$I_{C2}/I_{C1} = I_{S2}/I_{S1}$$


Beta mismatch Only

Since $I_S$ will be same and $V_{BE}$ is the same the measured $I_C$ will be the same so we do not detect any mismatch due to Beta mismatch.

Re Mismatch only














Setting $ΔI=I_{E1}{I_{E1}-I_{E2}}/I_{E1}≈I_{T}(1-I_{E2}/I_{E1})$

Solving for $I_{E2}/I_{E1}$:


Comparison of the Methods

Mismatch Factor Method 1 Method 2Comment
$I_S$$ΔV_{BE}=nV_TlnI_{S2}/I_{S1}$$ΔV_{BE}=V_Tln{I_{S2}}/I_{S1}$Both methods represent this mismatch
$β$$$ΔV_{BE}=nV_T{Δβ}/{β(1+β)}$$$ΔV_{BE}=0$Method 2 cannot measure the mismatch due to Beta
$R_E$$ΔV_{BE}=I_E(R_{E1}-R_{E2})$$ΔV_{BE}≈V_T{I_TΔR_E}/{nV_T+I_TR_E}$Method 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 $V_T$ dependance