Transistor Amplifier Supply For A LED

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{5}A_{51} Base Sequence = 12735 String Sequence = 12735 - 5 - 51**

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Transistor Amplifier Supply For A LED

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Figure 122.5 is a transistor amplifier circuit designed to supply a Light Emmitting Diode (LED). The output signal from the microcomputer acts as the switch for the LED. The circuit values are as follows:
**Microcomputer**: output resistance = R_{B} = 1 kΩ; V_{on} = 5 V; V_{off} = 0 V; current, I = 5 mA.
**Transistor**: V_{CC} = 5 V; offset voltage, V_{γ} = V_{BE} = 0.7;

Current gain, β = I_{C}/I_{B} = 95; V_{CEsaturation} =0.2 V.
**LED**: offset voltage, V_{γLED} = 1.4 V; I_{LED} > 15 mA; P_{max} = 100 mW.

(a)Determine collector resistance R_{C} such that the transistor is in the saturation region when the microcomputer outputs 5 V.

(b) Determine the power dissipated by the LED.

**The strings**:
S_{7}P_{5}A_{51} (Physical Change).
**The math**:

Pj Problem of Interest is of type *change* (physical change). Transistors are primarily used for signal *amplification* and *switching*. Both are *change* problems.

**(a)i** Computer is off = V_{off} = 0

So, Base current, I_{B} = 0

So, BJT is in the *cuttoff region*
**(a)ii** Computer is on = V_{on} = 5 V

At saturation and assumimg the large signal model we have:

V_{CC} = R_{C}I_{C} + V_{γLED} + V_{CEsaturation}

So, R_{C} = (5 - 1.4 - 0.2)/I_{C} = 3.4/I_{C}

I_{LEDmin} = 15 mA. So lets double this minimum current required to light LED

So, for 30 mA, R_{C} = (3.4/30)10^{3} = 113 Ω

Verifying BJT is in saturation region:

At saturation, β is significantly diminished.

I_{B} = (V_{on} - V_{BE})/R_{B}

So, I_{B} = (5 - 0.7)/1000 = 4.3 mA

β = 30/4.3 = 6.7.

So, since 6.7 << 95, BJT is operating plausibly in saturation region.
**(b)** Power disspated by LED = P_{LED} = V_{γLED}(I_{C}) = 42 mW

So, power dissipation of LED is less than power max of LED

So, design is ok.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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