Virtual Lab: C/N, FM Improvement & G/T

1. Laboratory Objectives

Understand the concept of Carrier-to-Noise Ratio (C/N) in satellite communication links and its significance in link budget design.
Learn how FM improvement factor enhances the baseband signal-to-noise ratio over the RF carrier-to-noise ratio.
Comprehend the G/T ratio (Figure of Merit) of a receiving earth station and its impact on overall link performance.
Investigate the FM threshold effect and the role of pre-emphasis and de-emphasis in satellite FM systems.
Measure and calculate C/N, FM improvement, and G/T using interactive simulations with realistic satellite link parameters.
Design a complete satellite downlink budget and determine the required earth station G/T for a given quality of service.

2. Theory

2.1 Carrier-to-Noise Ratio (C/N)

The Carrier-to-Noise Ratio (C/N) is the fundamental performance metric in satellite communications. It represents the ratio of received carrier power to the system noise power at the receiver input.

Basic Link Equation (Linear Form): C = P_t G_t G_r (λ / 4πd)² = EIRP · G_r / L_fs

Noise Power: N = k T_s B_n
where k = 1.38×10⁻²³ J/K, T_s = system noise temperature (K), B_n = noise bandwidth (Hz)

Carrier-to-Noise Ratio (Decibel Form): [C/N] = [EIRP] − [L_fs] + [G/T] − [k] − [B_n] (dB)

or equivalently:
[C/N] = [EIRP] − [L_fs] + [G/T] + 228.6 − 10·log₁₀(B_n) (dB)

Free Space Path Loss (FSPL): L_fs = 20·log₁₀(d) + 20·log₁₀(f) + 32.44 (dB)
d = distance (km), f = frequency (GHz)

_t+G_t Satellite Transponder Bent Pipe Earth Station RX G/T Figure Uplink L_fs,up + Atmospheric Loss Downlink L_fs,down + Atmospheric Loss Overall C/N is dominated by the downlink in most satellite systems

Figure 1: Satellite Communication Link showing Uplink and Downlink paths

Key Insight: In most satellite systems, the overall C/N is dominated by the downlink because the satellite has limited transmit power (EIRP) and the earth station receiver must detect very weak signals from 36,000 km away. The earth station G/T is therefore critical.

2.2 FM Improvement Factor

Frequency Modulation (FM) provides a significant SNR improvement over AM because the information is encoded in frequency variations rather than amplitude. The FM receiver uses a limiter to remove amplitude noise.

FM Improvement in dB (Unweighted): I_FM = 10·log₁₀(B/f_m) + 20·log₁₀(Δf/f_m) + 1.8 dB

Output Baseband SNR: (S/N)_out = (C/N)_in + I_FM + I_pre/de
I_pre/de ≈ 2.5 to 4 dB additional improvement with pre-emphasis/de-emphasis

_m B/2

Figure 2: FM noise power spectral density is parabolic. Pre-emphasis boosts high frequencies at TX; de-emphasis attenuates them at RX, reducing total noise.

2.3 G/T Ratio — Figure of Merit

The G/T ratio (Gain-to-Noise-Temperature ratio) is the standard figure of merit for a receiving system.

G/T Definition: G/T = G_ant / T_sys (K⁻¹)

[G/T] = [G_ant] − 10·log₁₀(T_sys) (dB/K)

System Noise Temperature: T_sys = T_ant + T_feed + T_receiver

T_feed = (L − 1) · T_phys (typically T_phys = 290K)

T_receiver = T_LNA + T₂/G_LNA + T₃/(G_LNA·G₂) + ... (Friis formula)

Antenna Gain: G = η · (πD/λ)²
η = aperture efficiency (~0.55–0.75), D = diameter (m), λ = c/f = wavelength (m)

Typical G/T Values: Large earth station (9m, 12 GHz): 35–40 dB/K. VSAT (1.2m, 12 GHz): 15–20 dB/K. LEO handheld terminal: −24 dB/K.

2.4 Pre-Emphasis and De-Emphasis

In FM satellite systems, thermal noise at the demodulator output has a parabolic spectral density. Pre-emphasis boosts high-frequency signal components at the transmitter before modulation. De-emphasis attenuates them by the same amount at the receiver after demodulation.

Pre-emphasis/De-emphasis Time Constant: τ = RC = 75 μs (standard for video) or 50 μs (standard for audio)
f_c = 1 / (2πτ) ≈ 2.12 kHz for τ = 75 μs

Important: Pre-emphasis and de-emphasis networks must be matched between transmitter and receiver. In satellite FDM-FM systems, CCIR-recommended networks provide approximately 2.3 to 2.6 dB of weighted SNR improvement.

2.5 FM Threshold Effect

FM systems exhibit a threshold effect: when the input C/N falls below approximately 10 dB, the output SNR degrades rapidly and non-linearly.

FM Threshold Condition: (C/N)_in ≥ 10 dB (typical threshold for conventional FM discriminators)

For FMFB or PLL demodulators, threshold extension to ~7–8 dB is possible.

Figure 3: FM demodulator output S/N vs input C/N. Below ~10 dB threshold, output quality collapses non-linearly.

2.6 Complete Satellite Link Budget

Overall C/N (Linear): (C/N)_overall⁻¹ = (C/N)_up⁻¹ + (C/N)_down⁻¹ + (C/N)_IM⁻¹

Overall C/N (dB) — Approximate when one link dominates: (C/N)_overall ≈ min[(C/N)_up, (C/N)_down] − small degradation

Parameter	Symbol	Unit	Typical Value
Boltzmann Constant	k	dBW/K/Hz	−228.6
Transmit Power	P_t	dBW	10–20 (Earth), 10–60 dBm (Sat)
Antenna Gain	G	dBi	50–65 (Large ES), 20–40 (Sat)
Free Space Loss (4 GHz, 36,000 km)	L_fs	dB	~196
System Noise Temp	T_s	K	50–150 (Clear sky)
RF Bandwidth	B	MHz	36–72 (Typical transponder)
Baseband Frequency	f_m	MHz	4–12 (FDM groups)

3. Interactive Simulations

Adjust the parameters in each simulation and observe the effects on C/N, FM improvement, and G/T in real time.

🔬 Sim 1: Satellite Link Budget & C/N Calculator

Transmit Power P_t (dBW)

Transmit Antenna Gain G_t (dBi)

Receive Antenna Gain G_r (dBi)

Frequency f (GHz)

Distance d (km)

System Noise Temp T_s (K)

Bandwidth B (MHz)

Miscellaneous Losses (dB)

📈 Sim 2: FM Improvement Factor Calculator

Peak Frequency Deviation Δf (kHz)

Max Baseband Frequency f_m (kHz)

RF Bandwidth B (kHz) — Carson's Rule: 2(Δf+fm)

Input C/N (dB)

Pre/De-emphasis Improvement (dB)

🛰️ Sim 3: G/T Figure of Merit Calculator

Antenna Diameter D (m)

Aperture Efficiency η

Frequency f (GHz)

Antenna Noise Temp T_ant (K)

Feed Loss L_feed (dB)

LNA Noise Figure NF (dB)

LNA Gain G_LNA (dB)

🌍 Sim 4: Complete Satellite Downlink Analyzer

This simulation combines all concepts: link budget, G/T, and FM improvement to show the complete signal quality chain from satellite to baseband.

Satellite EIRP

46 dBW

→

FSPL

196 dB

→

Atm. Loss

0.5 dB

→

Earth G/T

25 dB/K

→

C/N

17.1 dB

C/N (dB)

FM Imp. (dB)

Baseband S/N (dB)

Satellite Parameters

EIRP (dBW)

Frequency (GHz)

Distance (km)

Atmospheric Loss (dB)

Earth Station Parameters

Antenna Diameter (m)

Efficiency η

T_sys (K) — or use G/T directly

Override G/T (dB/K) — optional

FM Parameters

Bandwidth B (MHz)

Peak Deviation Δf (MHz)

Baseband f_m (MHz)

Pre/De-emphasis (dB)

Complete Link Analysis

Calculated Antenna Gain:—

Calculated G/T:—

FSPL:—

Received C/N:—

Modulation Index β:—

FM Improvement:—

Baseband Output S/N:—

Threshold Status:—

4. Experimental Procedure

Familiarization with Link Budget Parameters

Open Simulation 1. Review the default parameters representing a typical C-band satellite downlink (4 GHz, 36,000 km). Note the values of EIRP, FSPL, and expected C/N. Record these baseline values in your lab notebook.

Measure Carrier-to-Noise Ratio (C/N)

Vary the transmit power (P_t) from 0 dBW to 20 dBW in steps of 5 dB. Keep all other parameters constant. Record the resulting C/N and C/N₀ values. Plot C/N vs P_t and observe the linear relationship in dB.

Investigate the Effect of G/T

Using Simulation 3, vary the antenna diameter from 1 m to 10 m. For each diameter, calculate G/T. Then in Simulation 1, use these G/T values (by entering G_r and T_s appropriately) and record how C/N improves. Verify that doubling the antenna diameter increases G/T by 6 dB.

Analyze FM Improvement Factor

Open Simulation 2. Set a fixed input C/N of 16 dB. Vary the peak frequency deviation (Δf) from 200 kHz to 2000 kHz. For each value, record the modulation index β, FM improvement factor, and output S/N. Plot output S/N vs β and identify the region of linear improvement.

Demonstrate the FM Threshold Effect

In Simulation 2, set Δf = 750 kHz and f_m = 252 kHz. Gradually reduce the input C/N from 20 dB down to 0 dB in 2 dB steps. Observe how the output S/N behaves above and below the ~10 dB threshold. Record the C/N value at which the output S/N begins to collapse rapidly.

Evaluate Pre-emphasis/De-emphasis Benefit

Using Simulation 2 or Simulation 4, compare the output S/N with pre/de-emphasis improvements of 0 dB, 2.5 dB, and 4 dB. Record the improvement in baseband S/N for each case. Discuss why this improvement is most noticeable at the upper end of the baseband spectrum.

Complete Link Design Exercise

Using Simulation 4, design a satellite downlink to achieve a baseband S/N of at least 50 dB with the following constraints: Satellite EIRP ≤ 50 dBW, frequency = 12 GHz, bandwidth = 36 MHz, Δf = 18 MHz, f_m = 4 MHz. Determine the minimum required earth station antenna diameter and G/T. Verify your design by adjusting parameters until the target S/N is met.

Compare C-band vs Ku-band Performance

Using Simulation 4, compare two scenarios: (a) C-band at 4 GHz with 0.5 dB atmospheric loss, and (b) Ku-band at 12 GHz with 2.0 dB atmospheric loss. Keep all other parameters identical. Discuss the trade-offs in terms of antenna size, rain fade margin, and achievable C/N.

5. Guidelines for Report Writing

Your laboratory report should be a formal technical document following the structure below. Use clear headings, numbered figures and tables, and include units for all quantities.

5.1 Report Structure

Section	Content Requirements	Suggested Length
Title Page	Experiment title, student name, ID, date, course code, instructor name	1 page
Abstract	Brief summary (150–200 words) of objectives, methods, key results, and conclusions	½ page
Introduction	Motivation for C/N, FM improvement, and G/T in satellite communications. State the problem and objectives.	1–1½ pages
Theory	Derivation and explanation of: (i) Link budget equation, (ii) FM improvement factor, (iii) G/T ratio, (iv) Threshold effect, (v) Pre-emphasis/de-emphasis. Include all key equations with variable definitions.	3–4 pages
Simulation Setup	Description of the virtual laboratory environment. Tabulate all default parameter values used. Include screenshots of the simulation interface.	1–2 pages
Results & Discussion	Present all measured data in numbered tables and plotted graphs. Discuss trends: linearity of C/N with EIRP, quadratic FM improvement with β, threshold collapse, G/T scaling with antenna size. Compare theoretical predictions with simulation results.	4–5 pages
Design Exercise	Present your complete link design from Procedure Step 7. Show all calculations and justify your choice of antenna diameter, G/T, and margin.	1–2 pages
Conclusion	Summarize key findings. State what you learned about the relationship between C/N, FM improvement, and G/T. Discuss practical implications for satellite system design.	1 page
References	List all textbooks, papers, and online resources cited (IEEE format recommended)	½ page
Appendix	Include raw data sheets, additional plots, and sample calculations	As needed

5.2 Graphical Requirements

Graph 1: C/N (dB) vs Transmit Power P_t (dBW) — linear plot with theoretical slope = 1
Graph 2: Output S/N (dB) vs Input C/N (dB) for FM system — show threshold region clearly
Graph 3: FM Improvement Factor (dB) vs Modulation Index β — show theoretical 20log(β) trend
Graph 4: G/T (dB/K) vs Antenna Diameter (m) — log-log plot showing D² dependence
Graph 5: Baseband S/N (dB) vs Frequency with and without pre/de-emphasis

5.3 Assessment Rubric

Criterion	Excellent (A)	Good (B)	Satisfactory (C)	Poor (D)
Theory Presentation	All equations derived/ explained clearly with correct units	Most equations correct, minor gaps	Basic equations present, some errors	Major errors or missing equations
Data & Analysis	All data recorded, graphs well-labeled, trends analyzed deeply	Most data present, good analysis	Some data missing, superficial analysis	Incomplete data, no analysis
Design Exercise	Correct design with full justification and margin analysis	Correct design, limited justification	Partially correct design	Incorrect or missing design
Technical Writing	Clear, concise, well-organized, proper referencing	Good organization, minor errors	Adequate, some organizational issues	Poor organization, many errors

Tip: When presenting decibel quantities, always show the reference (e.g., dBW, dBi, dB/K). Remember that C/N is a dimensionless ratio expressed in dB, while G/T has units of dB/K. Never confuse C/N₀ (dB-Hz) with C/N (dB).

1. Laboratory Objectives

2. Theory

2.1 Carrier-to-Noise Ratio (C/N)

2.2 FM Improvement Factor

2.3 G/T Ratio — Figure of Merit

2.4 Pre-Emphasis and De-Emphasis

2.5 FM Threshold Effect

2.6 Complete Satellite Link Budget

3. Interactive Simulations

🔬 Sim 1: Satellite Link Budget & C/N Calculator

Results

📈 Sim 2: FM Improvement Factor Calculator

Results

🛰️ Sim 3: G/T Figure of Merit Calculator

Results

🌍 Sim 4: Complete Satellite Downlink Analyzer

Satellite Parameters

Earth Station Parameters

FM Parameters

Complete Link Analysis

4. Experimental Procedure

Familiarization with Link Budget Parameters

Measure Carrier-to-Noise Ratio (C/N)

Investigate the Effect of G/T

Analyze FM Improvement Factor

Demonstrate the FM Threshold Effect

Evaluate Pre-emphasis/De-emphasis Benefit

Complete Link Design Exercise

Compare C-band vs Ku-band Performance

5. Guidelines for Report Writing

5.1 Report Structure

5.2 Graphical Requirements

5.3 Assessment Rubric