# Chapter 13:Microwave Communication Link Basic Design Considerations¶

## Example 1,Page No:670¶

In [1]:
import math

# Variable Declaration
f       = 6;            # microwave terrestrial comm link oper. freq in Ghz
D       = 50;           # single hop path length in miles
# mid way of path length
D1      = 25;
D2      = 25;
N       = 3;            # N value for third fresnal zone

# calculations
F1      = 72.2*((D1*D2)/float((D*f)))**0.5;     # first fresnel zone
F3      = F1*math.sqrt(N);                    # Third fresnal zone

# Result
print'First Fresnel zone distance = %3.1f feet\n'%F1,'Third Fresnel zone distance = %3.1f feet\n'%F3;

First Fresnel zone distance = 104.2 feet
Third Fresnel zone distance = 180.5 feet



## Example 2,Page No:670¶

In [2]:
import math

# Variable Declaration
f       = 4.5;          # microwave terrestrial comm link oper. freq in Ghz
D       = 40;           # single hop path length in miles
hant    = 200;          # antenna ht. above surface of earth
# from fig
D1      = 5;
D2      = 35;
K       = 1;            # for normal case

# calculations
F1      = 72.2*((D1*D2)/float((D*f)))**0.5;     # first fresnel zone
# computing curvature 'h' of earth at a distance of 10 miles from Transmitter if given by (D1*D2)/(1.5*K)
h       = (D1*D2)/float((1.5*K));             # curvature of earth in feet
PLabove = hant - h;                    # path line is PLabove feet above surface of earth
hmaxtol = PLabove - F1;                # max tolerable height in feet

# Result
print'Maximum tolerable height of obstacle above surface of earth = %3.2f feet'%hmaxtol;

Maximum tolerable height of obstacle above surface of earth = 12.14 feet


## Example 3,Page No:671¶

In [5]:
import math

# Variable Declaration
f       = 4.5;          # microwave terrestrial comm link oper. freq in Ghz
D       = 40;           # single hop path length in miles
hant    = 200;          # antenna ht. above surface of earth
# from fig
D1      = 5;
D2      = 35;
K       = 2/float(3);            # K-factor

# calculations
F1      = 72.2*((D1*D2)/float((D*f)))**0.5;     # first fresnel zone
# computing curvature 'h' of earth at a distance of 10 miles from Transmitter if given by (D1*D2)/(1.5*K)
h       = (D1*D2)/float((1.5*K));             # curvature of earth in feet
PLabove = hant - h;                    # path line is PLabove feet above surface of earth
if PLabove < F1:
print'Available clearance above the surface of earth = %d feet'%PLabove,'\nRequired first fresnal zone clearance = %3.1f feet'%F1,'So it would be obstructed';

Available clearance above the surface of earth = 25 feet
Required first fresnal zone clearance = 71.2 feet So it would be obstructed


## Example 4,Page No:671¶

In [6]:
import math

# Variable Declaration
UF      = 2*10**-4;      # unavailability factor

# Calculations
outrage_t = UF*8760;    # outrage time in hours per year

# Result
print'Outrage time = %3.3f hours per year'%outrage_t;

Outrage time = 1.752 hours per year


## Example 5,Page No:671¶

In [7]:
import math

# variable Declaration
PL      = 50;       # path length in miles from fig
FM      = 40;       # fade margin in dB
P_fm_ex = 7*10**-5;  # prob. of fade margin getting exceeding
P_fm_ex_50db    = 6*10**-6;  # prob. of fade margin getting exceeding for fade margin 50dB
p_fig_30m_40db  = 2*10**-5;  # prob fig for patl length of 30miles and fade margin 40dB

# Calculations
impr_prob_a = P_fm_ex/float(P_fm_ex_50db);    # improvement in prob. of fade margin for a
impr_prob_b = P_fm_ex/float(p_fig_30m_40db);   # improvement in prob. of fade margin for b

# Result
print'(a):\n Improvement in probability of fade margin = %3.1f\n'%impr_prob_a,'(b):\n Improvement in probability of fade margin = %3.1f\n'%impr_prob_b;

(a):
Improvement in probability of fade margin = 11.7
(b):
Improvement in probability of fade margin = 3.5



## Example 6,Page No:672¶

In [8]:
import math
# Given data
UF_sh   = 0.01;     # unavail. factor for single hop
IF_SD   = 100;      # improvement factor due to space diversity

# Calculations
UF_4hl  = 4* UF_sh/float(100);     # unavail. factor for 4 hop link and conv from %
UF      = UF_sh/float((100*IF_SD)); # unavail. factor for single hop link if it employs space diversity

# Output
print'unavail. factor for 4 hop link = %3.4f\n'%UF_4hl,'unavail. factor for single hop link if it employs space diversity = %3.0e'%UF;

unavail. factor for 4 hop link = 0.0004
unavail. factor for single hop link if it employs space diversity = 1e-06


## Example 7,Page No:672¶

In [9]:
import math

# Variable Declaration
f       = 3.5;              # operating freq. of microwave link in Ghz
D       = 30;               # single hop path length in miles
a       = 1;                # roughness
b       = 0.5;              # humid climate
F       = 40;               # fade margin in dB

# Calculations
U       = a*b*2.5*10**-6 *f*D**3 *10**(-F/10);  # unavailability factor
U1      = U*525600;                             # unavailabilty factor in minutes per year
U4      = U1*4;      # unavailabilty factor for 4-hop link

# Result
print'Outage Time = %3.1f minutes per year'%U4;

Outage Time = 24.8 minutes per year


## Example 8,Page No:673¶

In [8]:
import math
# Given data
# D2 = 2*D1            # path length is doubled
# F2 = F1+10;          # fade margin is increased by 10dB
# f2 = 1.25f1          # frequency operation increased by 25 %

#(U1/U2)  = (f1* D1**3 * 10**(-F1/10))/ (f1* D1**3 * 10**(-F1/10))
# sub above values
#(U1/U2)  = (f1* D1**3 * 10**(-F1/10)) / (1.25*f1*8*D1**3*10**(-F1/10)*10**-1) = 1
print'Unavailability Factor remains unaltered';

Unavailability Factor remains unaltered


## Example 9,Page No:673¶

In [10]:
import math
# given data
print'The improvement factor is proportional to square of antenna spacing.Therefore,it will increase by a factor of 4\nConsequently,the unavailability factor and hence the outrage time will also reduce by a factor of 4';

The improvement factor is proportional to square of antenna spacing.Therefore,it will increase by a factor of 4
Consequently,the unavailability factor and hence the outrage time will also reduce by a factor of 4


## Example 10,Page No:677¶

In [11]:
import math
# Given data
DFM     = 40;       # dispersive fade margin
FFM     = 30;       # flat fade margin

# Calculations
CFM     = -10*math.log10(10**(-FFM/float(10)) + 10**(-DFM/float(10)));

# Output
print'Composite Fade Margin = %3.2f dB\n'%CFM;
print'minus sign is wrongly printed in Textbook';

Composite Fade Margin = 29.59 dB

minus sign is wrongly printed in Textbook


## Example 11,Page No:677¶

In [12]:
import math

# Variable Declaration
DFM1    = 50;       # dispersive fade margin
FFM     = 30;       # flat fade margin
DFM2    = 40;       # dispersive fade margin

# Calculations
CFM1    = -10*math.log10(10**(-FFM/float(10)) + 10**(-DFM1/float(10)));
CFM2    = -10*math.log10(10**(-FFM/float(10)) + 10**(-DFM2/float(10)));
d_CFM   = CFM1 -CFM2;

# Result
print'CFM increases by %3.2f dB for a 10 dB increase in DFM which is very Marginal'%d_CFM;

CFM increases by 0.37 dB for a 10 dB increase in DFM which is very Marginal


## Example 12,Page No:677¶

In [11]:
import math

# Variable Declaration
f       = 23;               # operating freq. of microwave link in Ghz
D       = 10;               # single hop path length in miles
a       = 1;                # topographic factor
b       = 0.5;              # climatic factor
DFM     = 40;               # dispersive fade margin
FFM     = 30;               # flat fade margin

# Calculations
CFM     = -10*math.log10(10**(-FFM/float(10)) + 10**(-DFM/float(10)));  # composite fade margin
U       = a*b*2.5*10**-6 *f*D**3 *10**(-CFM/float(10));     # unavailability factor
U1      = U*525600;                               # outrage time in min per year

# Result
print'Outrage time = %3.2f minutes per year'%U1;

Outrage time = 16.62 minutes per year


## Example 13,Page No:682¶

In [13]:
import math

# Variable Declaration
MTBF2    = 20000;       # microwave Tx output MTBF figure
MTBF3    = 60000;       # power amplifier portion of MTBF

# Calculations
MTBF1    = (MTBF2*MTBF3)/float((MTBF3-MTBF2));
impr     = MTBF1-MTBF2      # improvement in MTBF if power amplifier not used

# Result
print'Improvement in MTBF of transmitter if power amplifier is not used = %d hours'%impr;

Improvement in MTBF of transmitter if power amplifier is not used = 10000 hours