We submerge somewhat deeper into analysis of the seemingly simple TL431 voltage reference with transconductance amplifier to find that some useful design parameters are missing from the manufacturer specifications. Yet we can reconstruct them from the data that is given after reverse-engineering the test methods. The voltage gain is considered first.
Included in the TL431 model is the incremental output resistance,
Gm and ro are unspecified circuit parameters of the TL431. With some effort, both can be derived from part data.
The forward-path G = Gm x rout (see Seemingly Simple Circuits: The TL431 Voltage Regulator, Part 1 feedback block diagram) can be derived from data from the manufacturer gain-test setup. The incremental model is shown below, where the error summation is internal to the TL431. Added to the output of the block diagram in Part 1 is the voltage from a test source, νG , in series with RL which forms a resistive-divider block, Tg , driven by νG . Tg is a voltage divider comprised of RL and ro ||(R1 + R2 ). This circuit is used to find the closed-loop output resistance, rout (cl), and also can be used to find ro .
In the test circuit, RL = 232 Ω, R1 = 15 kΩ, and R2 = 8.25 kΩ. The divider, HV = 0.355, reduces loop gain, resulting in more variation in νE , for a larger measured voltage. The resistance at the output node is
The forward-path (open-loop) quasistatic (0+ Hz) voltage gain is experimentally determined from this circuit by the manufacturers to be
with RLG = 230 Ω. The specified typical value of G0 ranges as high as 1000 at a static output current of 10 mA. Other manufacturers give 500 or 600. The above value is on the low end of the range, taken from the quasistatic values on the gain-magnitude frequency plots as 52 dB.
The gain-test setup reduces the TL431 to a single-port circuit for incremental analysis because its VR input is constant (incrementally 0 V). The only varying input to the TL431 is consequently νb . The voltage gain, G , is determined by varying νG and measuring the resulting νO . Direct calculation of G can be made by also measuring νE ; then G = νO /νE .
A less direct calculation from νO is based on the feedback equations. The above test setup for voltage gain has a block diagram that adds Tg and νG to the TL431 feedback loop. The contribution of νG to νO (or Tg x νG ) is added within the loop because it affects the fed-back νO and is not isolated from the loop νO by a buffer stage.
The equations represented by the block diagram are
Solving for closed-loop νO and νE ,
The incremental values of the above voltages are their differentials, designated by lower-case subscripts:
The loop gain is G x HV and the closed-loop gain is
where the incremental νe = –νb . By measuring νg and νo , and knowing the resistor values, Tg and HV are also known. Then solving the above νo equation for G ,
Alternatively, by measuring νe and νo , then from the νe equation,
After ro is determined, Gm can then be calculated from the quasistatic G = G0 :
In Part 3, we continue our descent to the output resistance test and compare derived values to measurements.