### Path Loss Models for Microwave Links Unraveled

Free Space Model

The free space model only accounts for the loss in signal power due to spreading of energy over a 3-dimensional space.

### FSPL of FSL = (4*pi*f*d/c)^2

Where:
f - frequency
d - distance
c - speed of light
Wavelength (lambda) - c/f

We notice from the formula that as the frequency increases, the loss becomes greater, which is intuitive since more wavelengths are needed to cover a given distance compared to the lower frequency wavelengths. Naturally, as the distance increases, the loss becomes greater as well.

ITU Terrain Model

This model considers the Fresnel zone, aside from the free space loss at distances (-20*Cn+10) and closer (where Cn is the normalized terrain clearance).

### Total Loss = -20*Cn + 10 + FSL

Where:
Cn = (h1-h2)/sqrt((lambda*d1*d2/(d1+d2)));
h1 - height of LOS link
h2 - height of obstruction
d1 - distance to obstruction from TX 1
d2 - distance to obstruction from TX 2
lambda - wavelength

Weissberger's Model

-if (14<d<=400)

### Total Loss = FSL + 0.45*(f^0.284)*d

-if (0<d<=14)

Where:

d - depth of foliage along path

Once again, we observe that frequency and distance share a direct relationship with the total loss.

Hata Model (Urban)

### Path Loss in Urban Area = 69.55 + 26.16*log(f) - 13.82*log(hb) - Ch + (44.9 - 6.55*log(hb))*log(d)^b

Where:

f - frequency
hb - antenna height of base station
Ch - antenna height correction factor
d - distance
b - recommendation ITU-R P.529-3 Adjustment factor

Again, frequency and distance share a direct relationship with the total loss. However, the antenna height is also considered to decrease the loss (inverse relationship).

Hata Model (Suburban)

### Path Loss in Suburban Area = Path Loss in Urban Area - 2*log(f/28)^2-5.4

We can observe that the considered loss due to frequency is decreased with the suburban model.

Hata Model (For Open Areas)

### Path Loss in Open Area = Path Loss in Urban Area -4.78*log(f)^2 +18.33*log(f)-40.97

Cost 231 Extended Hata Model

### Total Loss = 46.33 + (44.9 - 6.55*log(hb))*log(d) + 33.9*log(f) - a(h) -13.82*log(hb) + C

hb - height of base station
h - mobile station height in meters
d - distance in kilometers
f - frequency in Megahertz
C = 0 for Suburban areas
C = 3 for Metropolitan Centers

Empirical Cost-Walfisch-Ikegami Model (Non-LOS)

### Total Loss = FSL + Rooftop-to-street diffraction loss + Multi-screen diffraction loss

Empirical Cost-Walfisch-Ikegami Model (LOS)

### Total Loss = 42.64 + 26*log(d) + 20*log(f)

Where:
d - distance in kilometers
f - frequency in megahertz

### Calculator Techniques for the Casio FX-991ES and FX-991EX Unraveled

In solving engineering problems, one may not have the luxury of time. Most situations demand immediate results. The price of falling behind schedule is costly and demeaning to one's reputation. Therefore, every bit of precaution must be taken to expedite calculations. The following introduces methods to tackle these problems speedily using a Casio calculator FX-991ES and FX-991EX.

►For algebraic problems where you need to find the exact value of a dependent or independent variable, just use the CALC or [ES] Mode 5 functions or [EX] MENU A functions.

►For definite differentiation and integration problems, simply use the d/dx and integral operators in the COMP mode.

►For models that follow the differential equation: dP/dx=kt and models that follow a geometric function(i.e. A*B^x).

[ES]
-Simply go to Mode 3 (STAT) (5)      e^x
-For geometric functions Mode 3 (STAT) 6 A*B^x
-(Why? Because the solution to the D.E. dP/dx=kt is an exponential function e^x.
When we know the boundary con…

### Common Difficulties and Mishaps in 6.004 Computation Structures (by MITx)

Updated:
May 6, 2018
VLSI Project: The Beta Layout [help needed]Current Tasks: ►Complete 32-bit ALU layout [unpipelined] in a 3-metal-layer C5 process. ►Extend Excel VBA macro to generate code for sequential instructions (machine language to actual electrical signals).
Current Obstacles/Unresolved Decisions:
►Use of complementary CMOS or pass transistor logic (do both? time expensive, will depend on sched.
►Adder selection: Brent-Kung; Kogge Stone; Ladner Fischer (brent takes up most space but seems to be fastest, consider fan-out) [do all? time expensive, will depend on sched.)
►layout requirements and DRC errors