At what voltages does the bias resistor built-in transistor (BRT) turn on and off?

The turn-on and turn-off thresholds are defined as “input voltage (ON)” (V_IN(ON)) and “input voltage (OFF)” (V_IN(OFF)) respectively in the datasheet.

• Input voltage (ON), V_IN(ON): Voltage required to obtain the collector current equal to or higher than the prescribed value (e.g., I_C ≥ 5 mA) at T_a = 25°C
• Input voltage (OFF), V_IN(OFF): Voltage required to keep the collector current below the prescribed value (e.g., I_C ≤ 0.1 mA) at T_a = 25°C

Let’s consider the case in which an NPN BRT turns on.
When the NPN BRT is off, its internal transistor Q is inactive. Therefore, the input voltage (V_I) applied to the B terminal is divided by R₁ and R₂ and then applied to the base (b) of Q. As V_I increases, the base-emitter (b-e) voltage (V_be) exceeds the threshold (typically 0.7 V), turning on Q. The input voltage (ON) is defined as the voltage required to provide a collector current of 5 mA or more, but the concept is the same.
Therefore, BRTs with a lower resistor ratio (R₁/R₂) reach the threshold voltage at a lower input voltage (V_IN(ON)). However, BRTs with a larger R₁ value provide lower I_B if their resistor ratio is equal.
For example, let the input voltage required to provide a collector current of 5 mA be VI1. Then, the base current ib and the b-e voltage Vbe of the built-in transistor are constant at ib1 and Vbe1 respectively regardless of the built-in resistance. Vin can be expressed as follows using these variables:
    V_in1 = R₁ * I_b1 + ( 1 + R₁ / R₂ ) * V_be
At a given resistance ratio, only the first term “R1 * Ib” on the right side changes. Therefore, it can be considered that Vin1 increases as R1 increases. (See Figure 3.)

Likewise, BRTs with a lower resistor ratio exhibit lower input voltage (OFF). However, the relationship between the resistor ratio and the input voltage (OFF) is less marked than the relationship between the resistor ratio and the input voltage (ON) because the test condition for the input voltage (OFF) is as low as 0.1 mA and therefore tends to be affected by device variations.

The above discussion also applies to PNP BRTs although their numeric sign is the opposite to that of NPN BRTs.

The I_C – V_I(ON) curves of Figure 2 show that the collector current changes suddenly at a given input voltage. The collector current also decreases as temperature increases. Make sure you allow for sufficient design margins.