We live in an era that each of us has few electronic devices in our household and office areas. These devices all operat
Posted: Tue Jun 07, 2022 11:48 am
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(2.4e9t) 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 A cos(2.4e9t) 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 aFrequencyC2 R1
V=Acos(ωt) Vc Frequency Low-pass L R1 V=Acos(ωt) VL(a) (b) (c)
Band- pass Frequency (d) Band-pass filter for your Wifi |Vc / V|
|Vo / V| 5GHz2.45 GHz (bluetooth) 28 GHz (5G technology)Center
frequency (fc) |Vo / V|V=Acos(ωt) V0 Z1 Z2 Z3 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 Bonus: A Very Simple Solution to an
Engineering Challenge (20 points) continued on next page. . .Page 6
of 7 Bonus: A Very Simple Solution to an Engineering Challenge (20
points) (continued) phone to only capture signals within a certain
frequency range and neglect everything else. As shown in Fig. 5(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. 5(b) behave at low frequencies and high frequencies?
Qualitatively draw the behavior of |VL/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. 5(c) (5 points).
• Write the phasor-domain expression of |V0/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).
(a) VAcont (c) 4|Vo/V V=Acos(wt) Band- pass |Vc/M Low-pass Center frequency (1) Frequency Z₂ Hu (b) IV./vt (d) 2.45 GHz (bluetooth) Frequency Figure 5: The circuit schematic V=Acos(wt) R₁ Band-pass filter for your Wifi 5GHz "Hell 28 GHz (5G technology) Frequency
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(2.4e9t) 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 A cos(2.4e9t) 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 aFrequencyC2 R1
V=Acos(ωt) Vc Frequency Low-pass L R1 V=Acos(ωt) VL(a) (b) (c)
Band- pass Frequency (d) Band-pass filter for your Wifi |Vc / V|
|Vo / V| 5GHz2.45 GHz (bluetooth) 28 GHz (5G technology)Center
frequency (fc) |Vo / V|V=Acos(ωt) V0 Z1 Z2 Z3 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 Bonus: A Very Simple Solution to an
Engineering Challenge (20 points) continued on next page. . .Page 6
of 7 Bonus: A Very Simple Solution to an Engineering Challenge (20
points) (continued) phone to only capture signals within a certain
frequency range and neglect everything else. As shown in Fig. 5(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. 5(b) behave at low frequencies and high frequencies?
Qualitatively draw the behavior of |VL/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. 5(c) (5 points).
• Write the phasor-domain expression of |V0/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 Operat 1 (62.26 KiB) Viewed 35 times