ece-1109 ECE-1109 Introduction to ECE The following examples illustrate the mathematical steps for the three Zener Diode Regulation cases, drawing directly from the procedures and equations outlined in the source notes.
- Case I: Fixed Input Voltage (V_i), Fixed Load Resistance (R_L)
This case determines the operating state of the Zener diode and calculates its operating parameters (V_L,I_Z,P_Z).
Example Setup:
• Input Voltage (V_i): 16 V
• Series Resistor (R): 1 kΩ
• Load Resistor (R_L): 3 kΩ
• Zener Voltage (V_Z): 10 V
Steps and Calculations:
| Step | Description | Calculation | Source(s) |
| 1. Test the State | Calculate the open-circuit voltage (V) across the Zener terminals using the voltage divider rule. | V=V_L=R+R_LR_LV_i=1 kΩ+3 kΩ3 kΩ⋅16 V=12 V | |
| 2. Determine “On” or “Off” | Compare the calculated voltage (V) with the Zener voltage (V_Z). | Since V=12 V is greater than V_Z=10 V, the Zener diode is “on.” | |
| 3. Calculate Parameters | Determine the load voltage, series current, load current, and Zener current. | V_L=V_Z=10 VI_R=RV_i−V_Z=1 kΩ16 V−10 V=6 mAI_L=R_LV_Z=3 kΩ10 V≈3.33 mAI_Z=I_R−I_L=6 mA−3.33 mA≈2.67 mA | |
| 4. Check Power Dissipation | Calculate the Zener power dissipation (P_Z). | P_Z=V_ZI_Z=10 V⋅2.67 mA≈26.7 mW |
- Case II: Fixed Input Voltage (V_i), Variable Load Resistance (R_L)
This case determines the minimum and maximum load resistance (RLmin to RLmax) required to maintain V_L=V_Z.
Example Setup:
• Input Voltage (V_i): 50 V
• Series Resistor (R): 1 kΩ
• Zener Voltage (V_Z): 10 V
• Maximum Zener Current (IZM): 40 mA
Steps and Calculations:
| Step | Description | Calculation | Source(s) |
| 1. Determine R_Lmin | Calculate the minimum load resistance, which occurs when I_Z≈0 A. This requires the load voltage (V) to equal V_Z. | RLmin=V_i−V_ZRV_Z=50 V−10 V(1 kΩ)⋅10 V=4010 kΩ=250 Ω | |
| 2. Calculate I_R | Calculate the total current flowing through the series resistor R (which is constant in this case). | I_R=RV_i−V_Z=1 kΩ50 V−10 V=40 mA | |
| 3. Determine ILmin | Calculate the minimum load current, which occurs at the maximum safe operation boundary, where I_Z=IZM. | ILmin=I_R−IZM=40 mA−40 mA=0 mA | |
| 4. Determine RLmax | Calculate the maximum load resistance corresponding to ILmin. | RLmax=ILminV_Z=0 mA10 V=∞ | |
| Result | The range of R_L for proper regulation (V_L=10 V) is: | 250 Ω≤R_L≤∞ |
- Case III: Fixed Load Resistance (R_L), Variable Input Voltage (V_i)
This case determines the minimum and maximum input voltage (Vimin to Vimax) required to keep the Zener regulated (V_L=V_Z).
Example Setup:
• Series Resistor (R): 220 Ω
• Load Resistor (R_L): 1.2 kΩ
• Zener Voltage (V_Z): 20 V
• Maximum Zener Current (IZM): 60 mA
Steps and Calculations:
| Step | Description | Calculation | Source(s) |
| 1. Determine V_imin | Calculate the minimum input voltage required to turn the Zener “on” (I_Z≈0 A). | Vimin=R_L(R_L+R)V_Z=1.2 kΩ(1.2 kΩ+0.22 kΩ)⋅20 V=23.67 V | |
| 2. Calculate I_L | Calculate the fixed load current. | I_L=R_LV_Z=1.2 kΩ20 V≈16.67 mA | |
| 3. Determine IRmax | Calculate the maximum permissible series current (I_R) when the Zener current is at its maximum rating (IZM). | IRmax=IZM+I_L=60 mA+16.67 mA=76.67 mA | |
| 4. Determine VRmax | Calculate the maximum voltage drop across R using IRmax. | VRmax=IRmaxR=(76.67 mA)⋅220 Ω≈16.87 V | |
| 5. Determine V_imax | Calculate the maximum input voltage, V_imax=V_Rmax+V_Z. | Vimax=16.87 V+20 V=36.87 V | |
| Result | The range of V_i for proper regulation (V_L=20 V) is: | 23.67 V≤V_i≤36.87 V |