(i) Design a non-inverting amplifier having a gain of 50 . Draw the circuit [ 4 pts .] and indicate the value of any components used [ 4 pts .]. (Use resistor values between \( 1 \mathrm{k} \Omega \) and \( 500 \mathrm{k} \Omega \).)

### Non-Inverting Amplifier Design with a Gain of 50 #### **Circuit Diagram** ``` +Vcc | | [ ] [ ] Op-Amp [ ] | |--------------------+ | | (+) (-) | | Vin | [Rf] | | | Out | | GND [Rg] | GND ``` #### **Component Values** - **Feedback Resistor (Rf):** 49 kΩ - **Ground Resistor (Rg):** 1 kΩ #### **Explanation** 1. **Op-Amp Configuration:** - The operational amplifier is configured in a **non-inverting** setup. 2. **Gain Calculation:** - The gain \( (A_v) \) of a non-inverting amplifier is given by: \[ A_v = 1 + \frac{Rf}{Rg} \] - To achieve a gain of 50: \[ 50 = 1 + \frac{Rf}{Rg} \implies \frac{Rf}{Rg} = 49 \] 3. **Choosing Resistor Values:** - Select \( Rg = 1\,k\Omega \) (within the specified range). - Then, \( Rf = 49\,k\Omega \) to satisfy the gain requirement. 4. **Connections:** - **Input Signal (Vin):** Connected to the non-inverting (+) input of the op-amp. - **Feedback Path:** A resistor \( Rf \) connects the output back to the inverting (-) input. - **Ground Resistor (Rg):** Connects the inverting (-) input to the ground. 5. **Operation:** - The non-inverting configuration ensures that the input signal is amplified without inverting its phase. - The resistors \( Rf \) and \( Rg \) set the desired gain of the amplifier. #### **Component Selection Summary** - **Operational Amplifier:** Any standard op-amp (e.g., LM741, TL081) - **Resistors:** - \( Rf = 49\,k\Omega \) - \( Rg = 1\,k\Omega \) - **Power Supply:** Appropriate voltage as required by the chosen op-amp (e.g., ±15V) This design ensures a stable non-inverting amplifier with a gain of 50 using resistor values within the specified range.