iTechGuides is reader-supported. When you buy through links on our site, we may earn an affiliate commission. As an Amazon Associate I earn from qualifying purchases. Learn more
FM’s familiar output-SNR improvement with increasing deviation ratio applies only when the received carrier-to-noise ratio (CNR) is high enough for the demodulator to remain above threshold. Below that region, noise can drive the received phasor close to the origin, causing rapid phase changes that a discriminator turns into large output spikes. A larger deviation ratio can improve output SNR above threshold, but it also widens the signal and can raise the CNR needed to use the conventional equation.
Why FM demodulation has a threshold
In a simplified receiver model, the desired carrier and noise add as phasors. When the noise is modest relative to the carrier, the resultant phasor stays near the carrier, and its phase changes track the transmitted modulation. As input CNR falls, noise can pull the resultant phasor near or around the origin. Near the origin, small noise changes can produce large, abrupt changes in the measured phase.
A frequency discriminator responds to the time derivative of phase. Those abrupt phase excursions therefore appear as large output spikes rather than as a small, proportional increase in ordinary noise. As Haykin and Moher explain, “Since angle modulation is a nonlinear process, demodulation of an angle-modulated signal exhibits a threshold effect.” The high-CNR output-SNR approximation does not describe performance reliably in this nonlinear region.
Choose a threshold convention before using the equations
There is no single sharp CNR value that marks threshold for every FM system: the practical boundary depends on the receiver and on the performance criterion. All About Circuits’ 2026 worked examples report different reference conventions—CNR 20 in its discussion of Haykin and CNR 10 in its discussion of Proakis—and use CNR 10 (a linear ratio, or 10 dB) for their calculations. The examples below use that convention as a design approximation, not as a universal guarantee.
#1 Best Overall
- 【Professional FM Radio Receiver】-- Facmogu FM radio receiver adopts professional Si4730 radio chip for better reception, higher signal sensitivity and better resistance to electrical interference. Also comes with 33ft long cable retractable antenna, you can position the antenna windowsill or rooftop(magnetic base helps you fix the antenna position), you can enjoy clear signal reception and explore various radio stations and enjoy your favourite programmes on different channels anytime, anywhere
- 【Support Global Frequency】-- Our Mini FM radio receivers feature a total of three sets of frequencies that support worldwide use, covering the standard FM radio bands of 64-108 MHz, 76-108 MHz and 87-108 MHz, ensuring that a wide range of stations
- 【Auto & Manual Search & Memory Function】-- Professional FM radio receiver with one rotary knob and two buttons which is very easy to use. Long press the rotary button to enter the manual frequency tuning function, long press the ATS button to enter the automatic station search function, long press the VHF to select the country frequency (three groups of frequencies, worldwide use), short press the VHF to store the station
- 【Minimalist Design】-- FM radio receiver is compact and sturdy with an black alloy case. Although there are few buttons, we have integrated almost all the adjustment functions above the rotary knob, you can easily control all the functions with this one knob.Long press the knob to enter the manual FM function, and short press the knob to enter the volume function, rotate the knob to adjust the volume or the station without any complicated buttons
- 【Package Content】-- 1 x FM radio receiver, 1 x USB -C cable, 1 x AV cable, 1 x 3.5mm audio cable, 1 x 10m retractable antenna, 1 x user manual. *Note: Combined with amplifiers, CD players and speakers, it delivers immersive sound performance to ensure an enjoyable listening experience
Let Ac be carrier amplitude, W the message bandwidth, D the deviation ratio, and N0 the one-sided noise power spectral density. The article defines baseband SNR as:
γ = Ac2 / (2N0W)
Its threshold condition is Ac2 / (2BTN0) ≥ 10. Using Carson’s bandwidth estimate BT = 2(D + 1)W gives:
γ ≥ 20(D + 1)
This relation makes the trade-off explicit: under the chosen convention, increasing D raises the minimum baseband SNR needed to stay at the estimated threshold boundary. Carson’s rule is a bandwidth measure, not a claim that an FM signal has a mathematically hard spectral cutoff; angle-modulated signals have theoretically infinite bandwidth.
The Tool Desk
Outbyte Driver Updater FREEFix the driver behind crashes, sound loss and screen glitchesFind Drivers →Outbyte PC Repair FREERepair Windows errors before they cause bigger problemsFix Now →Rank #2
- [FM Receiver for Best Reception] - NEWEST VERSION. The fm radio is a frequency modulated receiver designed according to meeting/rehearsal usage. This is a stereo radio, beautiful appearance, pocket size, sonorous sound. DSP digital processing technology chip is adopted, frequency modulation signal reception is stable. Increments: 0.1 MHz
- [User-friendly Radio] - With the 3.5mm stereo Earphone (include), you can enjoy stereo radio without affecting others, that is very user-friendly. With lock button function can avoid any error operation. Also, The personal radio have a preset function where you can save your favorite stations and jump back and forth between them. It can store 30 FM radio stations. Set two storage station methods, including manual and fully automatic.
- [Battery Operated, Sleep Timer] - Powered by 2 x AAA battery (not included).Highly recommend to keep one for emergency radio. Saved stations will not be lost due to shutdown or battery replacement. The pocket radio has a digital clock so you can get the time at any time. Also, 10-120 minutes auto shut-off lets you fall asleep to the radio without worry about waking up to dead batteries.
- [Ultra-Portable] - The handy size of 3.14x1.1x0.78 in and weight of 0.09 lb, equipped with a waterproof storage bag and lanyard, make it easier to carry and store. It's extremely compact, smaller than a deck of cards and will easily fit in a shirt pocket. This is perfectly sized for keeping in your glovebox, backpack, or tackle box to take fishing, camping, hiking or anywhere.
- [Simple Operation, High Quality Guarantee] - No complicated operations, power on the radio and ready to go.Great for senior, elderly person and parents. It is suitable for home, traveling, camping, hiking, walking, bicycle, etc. If there is any problem with the product, please contact us and we will give a satisfactory solution. a full 12-month guarantee and 24-6 customer service if you encounter question.
How deviation ratio affects output SNR and bandwidth
For the high-CNR approximation used in the worked examples, output SNR is:
SNRout = 3D2γ · Pm / (max |m(t)|)2
Here Pm is message-signal power, and max |m(t)| is its peak magnitude. For a fixed message and input SNR, the expression predicts an output-SNR increase proportional to D2. But D also increases Carson-rule bandwidth, BT = 2(D + 1)W, and the adopted threshold condition requires γ ≥ 20(D + 1). Consequently, the output-SNR formula cannot be used to claim that any desired D is feasible at a given carrier power.
Keep PSD conventions consistent when substituting values. If a problem gives the two-sided density N0/2, convert it to the one-sided N0 used above. For example, N0/2 = 10−8 W/Hz corresponds to N0 = 2 × 10−8 W/Hz.
Rank #3
- Bass & Treble Control】Designed with volume, treble and bass control knobs for more delicate adjustment of the sound, much fun and high playability. Include controller for distant audio adjustments. Note: There is an isolation plastic sheet at the bottom of the remote control, which needs to be removed before use.
Worked example: minimum power without a channel-bandwidth limit
All About Circuits’ 2026 example assumes W = 10 kHz, normalized message power Pm/(max |m(t)|)2 = 0.5, two-sided noise PSD N0/2 = 10−8 W/Hz, and target output SNR 40 dB (= 104). With no channel-bandwidth limit specified, first solving the output-SNR equation alone gives a trial deviation ratio of D = 15, γ ≈ 29.6, and carrier power Ac2/2 = 5.92 mW.
That trial point is below the adopted threshold: at D = 15, the criterion requires γ ≥ 20(15 + 1) = 320, not about 29.6. The high-CNR output-SNR calculation therefore cannot justify the 5.92 mW result.
Solving at the adopted threshold boundary instead gives D = 6.6, γmin = 20(6.6 + 1) = 152, and carrier power Ac2/2 = 30.4 mW. This is an illustrative minimum under the example’s model and CNR convention. A practical design would normally allow margin rather than rely on operating exactly at an approximate threshold boundary.
Rank #4
- Mini stereo FM receiver module adopts advanced DSP and PLL technology ensure high quality broadcast receiving performance
- Blue backlight LCD display and potentiometer regulate the volume and frequency easy to operation
- On-board 2X3W stereo audio amplifier chip enable you to DIY FM radio easily, no extra audio amplifier circuit needed
- Working Voltage: DC 3-5V, Frequency Range: 50Hz-18KHz, Output Power: 500mW, Board Size: 75 X 45 X 30mm/2.95 X 1.77 X 1.18inch
Worked example: a 100 kHz channel limit
With the same message, noise, and 40 dB output-SNR target, a 100 kHz channel limit constrains the deviation ratio through Carson’s rule:
100 kHz = 2(D + 1)(10 kHz), so D = 4.
Applying the output-SNR equation at D = 4 gives γ ≈ 416.6 and carrier power Ac2/2 = 83.3 mW. The smaller permitted deviation ratio provides less noise improvement, so more carrier power is required to meet the same output-SNR target. This comparison shows why deviation ratio, bandwidth, and carrier power must be designed together rather than ranking D in isolation.
Crashes, No Sound, or Screen Glitches?
Random freezes, missing sound and display glitches usually trace back to one bad driver. Find and replace yours safely.Free scan · under a minutePC Slower Than It Used to Be?
A free scan shows the junk files, broken settings and background clutter dragging Windows down - then fixes them in one click.Free scan · Windows 10 & 11| Design case | Deviation ratio | Input baseband SNR γ | Carrier power | Interpretation |
|---|---|---|---|---|
| Unconstrained trial, before threshold check | 15 | ≈29.6 | 5.92 mW | Fails the adopted threshold requirement of 320. |
| Unconstrained threshold-boundary solution | 6.6 | 152 minimum | 30.4 mW | Approximate minimum under the example’s convention. |
| 100 kHz channel limit | 4 | ≈416.6 | 83.3 mW | Meets the stated output-SNR target with the bandwidth-constrained deviation ratio. |
Worked example: minimum test-generator signal level
The same 2026 article estimates a minimum FM test-generator signal using a 200 kHz FM bandwidth, 300 Ω source and receiver input resistances, a 290 K source noise temperature, and a 250 K receiver noise temperature. Under its matched available-noise-power model, it adds the source and receiver equivalent temperatures, then calculates noise power kTB = 1.49 × 10−15 W. Using the selected CNR of 10 gives minimum signal power 1.49 × 10−14 W, or −108.3 dBm, and carrier amplitude of about 3 μV into 300 Ω.
Best Value
- HIGH POWER 400W AMPLIFIER: AMP10 amplifier home audio connects with common 4–16Ω passive speakers, delivers 400W power amplifier peak output with 50W+50W rated power, and supports FM, USB, SD, AUX, and Bluetooth inputs for music playback, TV audio, and movies, meeting daily home audio needs
- MIC INPUT AND ECHO CONTROL: AMP10 stereo audio amplifier includes 2 microphone input ports with independent echo and mic volume adjustment, allowing users to speak or sing while music is playing, making it easy to use for home karaoke, family gatherings, or small parties
- BLUETOOTH 5.0 SIGNAL: AMP10 2 channel stereo receiver with bluetooth 5.0 supports wireless music playback from phones and tablets within about 50 ft, with signal-to-noise ratio above 85 dB and distortion below 0.5%, stable connection for a smoother everyday experience in amplifier home audio use
- BLUETOOTH 5.0 SIGNAL: AMP10 audio component amplifiers support Bluetooth 5.0 wireless music playback from phones and tablets within about 50 ft, with signal-to-noise ratio above 85 dB and distortion below 0.5%, stable connection for a smoother everyday experience
- CUSTOM TONE CONTROL: AMP10 stereo audio amplifier includes independent bass and treble knobs to adjust sound for different music styles, movies, or spoken audio, and comes with a remote control to make adjustments more convenient (requires 2×1.5V AAA batteries, not included)
Those values depend on the stated temperature, resistance, bandwidth, matched-noise model, and chosen threshold CNR. They are not a universal receiver sensitivity specification.
What can extend the usable threshold region?
Receiver design can reduce the impact of noise at the discriminator or improve demodulation behavior, but these techniques do not make the conventional high-CNR equation valid below threshold.
- Predetection filtering: Restricting the bandwidth ahead of the discriminator can reduce the noise entering it. A Government of Canada technical report describes this approach as a way to extend the FM threshold region.
- FM feedback demodulation: FM feedback is identified as a threshold-extension approach in the All About Circuits article.
- PLL demodulation: A phase-locked-loop receiver is another threshold-extension option identified there.
These are alternative receiver structures or noise-management techniques, not interchangeable numerical corrections to the threshold relation. Their performance depends on implementation and operating conditions.
Free tools Windows power users keep installed
One-click scans. No signup required.
Further reading
For the phasor explanation and a fuller treatment of FM threshold behavior, see Haykin and Moher’s Principles of Communications, 6th edition, section 7.4, “Threshold Effect in FM Demodulation.” NASA’s Technical Reports Server also records J. Duncan’s 1964 report, “FM demodulator threshold reduction final report”, on predetection filtering to reduce noise at the discriminator input.
Quick Recap
Product prices and availability are accurate as of the date/time indicated and are subject to change. Any price and availability information displayed on Amazon at the time of purchase will apply.
