Learning Goal: This problem shows how the power dissipated in the load depends on the value of the load resistance. It also helps to understand the condition required for maximum power transfer. Smartphones use "bars" to indicate strength of the cellular signal. Fewer "bars" translate to slow or no connectivity. But what do these "bars" actually stand for? Voltage, current? Well, not quite. Good radio (a cellular modem is a particular type of radio) reception depends on the power received at the receiver. Communication theory tells us that higher received signal power enables higher data rates. To that end, we design a receiver that maximizes the power received, and hence connection speed. A typical receiver consists of an antenna and receiver circuits. The antenna receives the radio waves propagating in space, and converts it into electrical voltages and currents. A very good abstraction used by circuit designers is to model the antenna as a voltage source Vs, with a series resistance Rs. The typical values of Vs in a real cellular receiver are in the range of micro- or milli-volts (10-“ and 10-, respectively) and the typical values of resistance Rs are usually 502 or 752, depending on how the antenna is designed. The receiver circuits are quite complex and will be covered in detail in EE142 "Integrated Circuits for Communications". However, a standard abstraction is to model these receiver circuits as a load resistance Rz to the antenna, as shown in the figure below. Receiver Circuits Antenna Models are very important in engineering design for their ability to abstract away details when they are not needed and are the key to successful design of complex systems We will discuss the use and propertices of electronic circuit models further in class. Use the following component values for your calculations: Vs = 100pV, and Ry = 502. (a) Consider any value of R2 within the range: OS RL S m. Find the value of R. that maximizes the voltage V. across resistor R1. Calculate the values of V.z., It, and the power P. dissipated by resistor R1. for the value you found. (Hint: The antenna voltage Vs and the resistance Rs are fixed. However, you are free to choose the value of Ry in order to maximize the voltage Vz. Alternatively, you may also intuitively argue for a particular value of Ry. How does the voltage across a resistor change as the value of the resistor increases?) (b) Consider any value of R. within the range: 0 5 RL Sm Find the value of R2 that maximizes the current lz through resistor R1. Calculate the values of Vz. IL, and the power P. dissipated by resistor R for the value you found. (Hint: The antenna voltage Vs and the resistance Rs are fixed. However, you are free to choose the value of Ry in order to maximize the current 14.) (c) Find the value of Ry that maximizes the power P, delivered to resistor R1. Calculate the values of V. IL, and the power P delivered to resistor R. It is important to note that this value of R which maximizes the power delivered to R, aso optimizes cellular connectivity. (Hint: The power optimization is best performed algebraically by setting the derivative of Pr. with respect to R1. to 0. Alte da the Plat B