# NPN BJT Node Voltages Analysis Given measured voltages (with respect to ground): - \( V_B = 2.1\,\mathrm{V} \) - \( V_C = 6.3\,\mathrm{V} \) - \( V_E = 1.5\,\mathrm{V} \) --- ## a) Mode of Operation ### Step 1: Calculate Junction Voltages - **Base-Emitter Voltage:** \( V_{BE} = V_B - V_E = 2.1\,\mathrm{V} - 1.5\,\mathrm{V} = .6\,\mathrm{V} \) - **Base-Collector Voltage:** \( V_{BC} = V_B - V_C = 2.1\,\mathrm{V} - 6.3\,\mathrm{V} = -4.2\,\mathrm{V} \) - **Collector-Emitter Voltage:** \( V_{CE} = V_C - V_E = 6.3\,\mathrm{V} - 1.5\,\mathrm{V} = 4.8\,\mathrm{V} \) ### Step 2: Determine Mode - \( V_{BE} \approx .6\,\mathrm{V} \): Base-emitter junction is **forward biased**. - \( V_{BC} < \): Base-collector junction is **reverse biased**. **Conclusion:** The BJT is in the **active (forward-active) mode**. --- ## b) Junction Bias Condition Justification - **Base-Emitter Junction:** - Forward biased if \( V_{BE} > \) (typically \( \approx .6 - .7\,\mathrm{V} \) for Si BJTs). - Here, \( V_{BE} = .6\,\mathrm{V} \) ⟹ **Forward biased**. - **Base-Collector Junction:** - Reverse biased if \( V_{BC} < \). - Here, \( V_{BC} = -4.2\,\mathrm{V} \) ⟹ **Reverse biased**. **Summary Table:** | Junction | Calculated Voltage | Bias Condition | |--------------------|-------------------|------------------| | Base-Emitter (\(V_{BE}\)) | \(.6\,\mathrm{V}\) | Forward biased | | Base-Collector (\(V_{BC}\)) | \(-4.2\,\mathrm{V}\) | Reverse biased | **Thus, the BJT is in active mode.** --- ## c) Collector Current Calculation (\( \beta = 150 \)) ### Step 1: Calculate Emitter Current Assume base-emitter forward voltage drop is \( V_{BE} = .6\,\mathrm{V} \). For a silicon BJT, \[ I_E \approx \frac{V_{BE}}{r_e} \] But typically, current is determined by the base resistor or circuit details, which are not given. Instead, use the relationship between \( I_C \) and \( I_B \): \[ I_C = \beta I_B \] But first, calculate \( V_{BE} \) to find \( I_B \): Assuming a typical base-emitter diode equation: \[ I_B = \frac{V_{BE} - V_{\text{on}}}{R_B} \] But \( R_B \) is not provided. **However, if only mode and currents are asked:** - **In active mode:** \[ I_C = \beta I_B \] Since \( I_E = I_C + I_B \), but without \( I_B \) or an external resistor value, we cannot numerically calculate \( I_C \) further. **If you assume a typical base current (or if more info is provided), substitute here.** **With only the voltages and \( \beta \), collector current cannot be numerically computed without more circuit details (like base resistor or input current).** --- ### **Summary Table** | Parameter | Value / Result | |---------------------|--------------------------------------| | Mode | Forward-active | | \( V_{BE} \) | \( .6\,\mathrm{V} \) (Forward) | | \( V_{BC} \) | \( -4.2\,\mathrm{V} \) (Reverse) | | \( I_C \) | \( I_C = \beta I_B \) (Need \( I_B \)) | --- **If you have base current or resistor data, plug it in for a numerical \( I_C \).**