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phone to only capture signals within a certain frequency range and neglect everything else. As shown in Fig. (a), we observed in lecture 20 that a RC connection can behave like a low-pass filter (passing the lower frequencies and stopping the higher frequencies). This low-pass filter solves the problem for interfering unwanted signals at higher frequencies (e.g., 5th generation signals at 28 GHz) but does not help much about the low-frequency interference. • How does the RL combination shown in Fig. [(b) behave at low frequencies and high frequencies? Qualitatively draw the behavior of V₁/V (5 points). • Use a combination of R, L, and C instead of Z₁, Z₂, and Z3 that generates a qualitative band-pass-look profile shown in Fig. (c) (5 points). • Write the phasor-domain expression of Vo/V for the filter you designed in the previous part and choose arbitrary values of R, L, C, such that your bandpass filter has its center frequency at 5 GHz (you have just upgraded your internet provider who offers 5 GHz wifi connections). We only focus on center-frequency now and we do not care about the sharpness of the filter. This is our first trial (5 points).

We live in an era that each of us has few electronic devices in our household and office areas. These devices all operate based on the fundamental theorems that we have learned in this class and mostly enable wireless connections. For example, your Wifi modems may operate at 900 MHz, 2.4 GHz, 3.6 GHz, 4.9 GHz, 5 GHz, 5.9 GHz. This means that your laptop/phone and the wifi modem will establish a wireless connection at one of these frequencies. You can assume that in the case of 2.4 GHz, the router transmits a signal in the form of V(t) = A cos(2.4e³t) and the cellphone receives it. As soon as this signal is received by your phone, a connection is established and you are connected to Wifi. The situation is actually not this simple. In fact, you should all have heard about the internet bandwidth" which is directly impacting the download/upload speed of your connection. The bandwidth is defined as the difference between the highest and lowest frequencies that a signal covers. In fact, your Wifi router, instead of transmitting Acos(2.4e³t) transmits a signal that has all the frequencies from 2.3 GHz to 2.5 GHz. In this case, we say that the bandwidth is 200 MHz and this is perhaps close to the numbers that you have heard from internent providers about the internet speed. The larger the bandwidth, the faster your internet connection is. Obviously, you are not the only person establishing a wireless network in your household. Perhaps a IVE/V AV₂/V LAL 20 GHz (30 Center Figure 5: The circuit schematic family member is listening to music with a bluetooth headset which operates at 2.45 GHz. And many other electromagnetic signals flowing in the environment that we do not see but your wireless devices will definitely capture them. If a wifi signal and a bluetooth signal are both captured with your phone wifi receiver, your internet speed drops, and you might even lose it if the received bluetooth signal is much stronger than the desired Wifi signal (naively saying, it has a larger amplitude A). And this is the reason that every time you board a plane, you are asked to turn-off your cell-phones. The wireless signals of 200-300 passengers' cellphones or even few of them could be strong enough to interfere with the pilot control/navigation wireless transceivers which could lead to the loss of navigation signals. This is where the importance of so-called "bandpass filters" shows up. Essentially, your phone that is connected to wifi would like to only care about frequencies that the Wifi router is transmitting and does not like to receive anything from the bluetooth signals, fast 5th generation internet signals (28 GHz), Walkie- talkie (136-900 MHz), etc. Therefore, bandpass filters are developed which allow the Wifi receiver on your Sand-