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If the VCE(sat) of a bias resistor built-in transistor (BRT) does not drop to the design target because of a heavy load, what can I do?

Figure 1 BRT circuit
Figure 1 BRT circuit

Figure 1 shows a simple BRT circuit. RO is a pull-up resistor for the BRT, and ZL is the load impedance. For the sake of simplicity, ZL is considered an impedance (resistance) expressed as a real number.
In this case, while Q is on, the collector-emitter voltage must satisfy the low-level voltage requirement for the following circuit.

First, let’s consider a circuit without ZL.
Without ZL, the collector-emitter saturation voltage (VCE(sat)) of the internal transistor (Q) is expressed as a function of the collector current (IC):
    VCE(sat) ≈ RO * IC

When ZL is connected to the BRT, the combined impedance seen from the collector of the BRT is:
    Z = RO // ZL = RO * ZL / ( RO + ZL ) 
The collector-emitter voltage (VCE) due to this combined impedance is expressed as follows:
    VCE = Z * IC
VCE must satisfy the low-level voltage requirement of the following circuit. Otherwise, it is necessary to increase the collector current by increasing the base current (Ib) of the internal transistor.
Ib can be increased in the following ways:
    1. Increase the input voltage (VI).
    2. Replace the BRT with the one having a smaller R1 value.
    3. Replace the BRT with the one having a larger R2 value.

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