ADC Spurious Calculator

Introduction to Spurious-Free Dynamic Range (SFDR) in ADCs: Definition and Theory

Definition:Spurious-free dynamic range (SFDR) is the ratio of the amplitude of the fundamental frequency component of the output signal to the amplitude of the largest spurious signal component—harmonic or otherwise—present within the specified bandwidth. This metric is typically expressed in dBc (decibels relative to the carrier).

Your dynamic range and signal integrity are fundamentally governed by the SFDR of your analog-to-digital converter (ADC). In high-end RF systems, especially within 5G radios and modern communications architectures, a critical specification for your PLL and clocking circuitry is the spur amplitude it can tolerate without violating the required sfdr. Unwanted frequency artifacts—sometimes called intermodulation products or harmonics—can arise from clock feedthrough, quantization, spectral leakage, intermodulation products, or power supply coupling, so understanding their impact is crucial for both system budget planning and receiver sensitivity.

Key Spurious Factors: Signal-to-Noise Ratio, Noise Figure, and Quantization

Signal-to-noise ratio (SNR)

SNR quantifies how much the desired signal exceeds the sum of system noise—both quantization and analog sources. For an ideal N-bit ADC: $$ \text{SNR}_{\text{quantization}} = 6.02N + 1.76 \ \text{dB} $$ where N is the ADC resolution in bits.

Noise figure (NF)

Represents the degradation of the SNR that arises as the signal passes through the ADC. Key to cascade analysis in receiver design, it's defined as: $$ \text{NF}_{\text{ADC}} = \text{SNR}_{\text{reference}} - \text{SNR}_{\text{ADC}} $$ where the reference is normally thermal noise (kTB).

Quantization noise

Quantization inherently adds white noise, distributed across the Nyquist bandwidth, setting a theoretical noise floor and impacting SFDR. The root-mean-square (rms) error is given by: $$ \text{A}_{\text{QUANT (rms)}} = \frac{\text{LSB}}{\sqrt{12}} $$

The Role of THD, SINAD, and Intermodulation Distortion in Spurious Analysis

• Total Harmonic Distortion (THD): The ratio of the root-sum-square power of all harmonics above the fundamental to the power in the fundamental frequency, accounting for nonlinearity errors in ADC or DAC:

THD (dB) = \( 20 \log_{10} \left( \frac{\sqrt{V_{2}^{2} + V_{3}^{2} + ... + V_{n}^{2}}}{V_{1}} \right) \)

• SINAD (Signal-to-Noise and Distortion Ratio): Measures the total unwanted energy (noise + distortion) present with respect to the fundamental.
• Intermodulation Distortion (IMD): Arises from multi-tone (two-tone or more) input signals, producing frequency components at sums and differences of the original tones, which can dominate spurious performance in wideband or multi-signal environments and is a key factor in transmitter front-ends and radio architecture.

Formulas and Equations for Spur Analysis and SFDR

See key equations for spurious analysis, SFDR, and system specification

• SFDR from FFT/DFT Measurement (in dBc): $$\text{SFDR}_{\text{dBc}} = 20 \log_{10} \left( \frac{A_{\text{fundamental}}}{A_{\text{largest spur}}} \right) $$
• SNR due to quantization noise: $$\text{SNR}_{\text{dB}} = 6.02N + 1.76 $$
• Noise Figure of an ADC: $$\text{NF}_{\text{ADC}} = \text{SNR}_{\text{reference}} - \text{SNR}_{\text{ADC}} $$
• PLL Spur Requirement Equation: $$ \text{Spur}_{\text{allowable}} = \text{SFDR}_{\text{required}} + 20 \log_{10} \left( \frac{F_{\text{signal}}}{F_{\text{clock}}} \right) $$ Where \( F_{\text{signal}} \) is the fundamental output frequency and \( F_{\text{clock}} \) is your sampling clock frequency.

Worked Example 1: Calculating SFDR for a 12-bit ADC in a Narrowband Receiver

1. Set variables: \( N = 12 \) bits, full-scale input tone, measured largest spurious signal (spur) = -70 dBc.
2. Apply SFDR measurement: Use FFT to locate the amplitude of fundamental and largest unwanted artifact among output tones.
3. Calculate SFDR: If fundamental = 0 dBc, largest spur at -70 dBc,
   $$ \text{SFDR} = 70\ \text{dBc} $$
4. Interpretation: This SFDR means your ADC will allow signals down to 70 dB below the carrier without interference from spurious components within the receiver bandwidth.

Worked Example 2: Assessing Impact of Two-Tone IMD on Spurious Performance

1. Test setup: Two input tones at frequencies \( f_{1} = 10 \text{MHz} \), \( f_{2} = 10.1 \text{MHz} \), full-scale amplitude for both.
2. Measurement procedure: Use FFT (or DFT) to identify intermodulation products at \( 2f_{1} - f_{2} \), \( 2f_{2} - f_{1} \), etc.
3. Quantify IMD: Suppose worst intermodulation spur is at -65 dBc relative to the larger tone.
4. SFDR impact: The SFDR in the presence of this two-tone input is limited to 65 dBc, dominated by IMD.
5. Conclusion: For multi-tone or wideband signal applications, intermodulation distortion artifacts often determine the effective SFDR.

Worked Example 3: Applying the ADC Spurious Calculator to Compare PLL Spur Requirements

1. Input parameters for wideband scenario: Target SFDR = 60 dBc, output frequency = 350 MHz, input clock = 1966.08 MHz (typical in 5G base station systems).
2. Calculate allowable PLL artifact: $$ \text{Spur}_{\text{max}} = -60 + 20 \log_{10} \left( \frac{350}{1966.08} \right) $$
3. Numerical value: $$ = -60 + 20 \log_{10}(0.178) = -60 - 15 = -75\ \text{dBc} $$
4. Interpretation: The PLL in this wideband context cannot have any clock spurs above -75 dBc to ensure the ADC's SFDR isn't degraded.
5. Compare with narrowband: For a narrowband device (e.g., 10 MHz output), allowable artifact is: $$ -60 + 20 \log_{10} \left( \frac{10}{1966.08} \right) \approx -60 - 46 = -106\ \text{dBc} $$
6. Resulting consideration: Tighter constraints for narrowband operation necessitate higher-performing PLL architectures, often at increased design and cost complexity.

Comparative Overview of SFDR and Key Performance Metrics for Selected ADCs

ADC Model	Resolution (bits)	Fs (MSps)	SFDR (dBc)	SNR (dB)	SINAD (dB)	THD (dB)	IMD (dB)	Noise Figure (dB)	ENOB
ADS4149	16	250	82	73	72	-85	-90	9.3	11.5
MAX1448	10	80	78	58.4	57	-61	-67	13.5	9.4
Generic 12-bit, High-Speed ADC	12	100	70	67.2	66	-78	-80	15.4	10.8

Practical Resources and Tools for Spur Analysis Using the ADC Spurious Calculator

ADC Spurious Calculator: Features and Usage Guide

The adc spurious calculator is specifically designed to simplify analysis and system specification of spur and SFDR requirements for professional RF, digital, and high-speed electronics applications. It considers all the critical variables—input tone, output frequency, sampling clock, bandwidth, and measured or desired SFDR—and produces quantitative outputs for system requirement comparison. Whether you are specifying a pll spur requirement, selecting a spectrum analyzer, or benchmarking dynamic range of competing data converters, this free calculation tool streamlines your process, allowing you to account for input resistance, output signal, and even ohms when considering analog signal sources.

Available for free

There are no registration or paywall requirements to use this tool. It is provided as a quick-reference resource to support technical decisions at any stage of your project.

Key calculation variables

Adjust full-scale input voltage, sampling rate, number of bits (n), measured spurious artifact amplitude, and your application signal range for tailored insight.

• Supports analog-to-digital conversion, digital-to-analog, and composite signal chain analysis using a2d and mixers as signal processing elements.
• Generates comparative tables for real-world device benchmarking, supporting transmitter and radio designers.
• Provides actionable recommendations on spurious constraint for high end communications and signal processing.
• Compatible with raw decibel, milliwatt, or dBm units.
• Applies calibrated data sources from datasheets, vendors, and academic sources to help analyze rf electrical performance when design is critical.

Further documentation and advanced data converter resources

• Analog Devices: Defining and Testing Dynamic Parameters in High-Speed ADCs (Reference material, data acquisition, instrumentation)
• Texas Instruments: Impact of Sampling-Clock Spurs on ADC Performance (engineering)
• RF Cafe: A/D Converter Calculations for RF Applications (calculations and formulas)
• High Frequency Electronics: RF Design Calculators and Tools
• Apex Waves: Free Bench-Ready Tools for DAQ, RF work, and power electronics
• Maxim Integrated: Engineering Calculators and Reference Documentation

Supplementary Engineering Resources and Tools

• Datasheets: Review manufacturer datasheet support for actual laboratory results and dynamic criterion values. Consult Analog Devices, Texas Instruments, Maxim Integrated, and other major semiconductor vendors for background material, calibration standards, and test procedures specific to your process or data acquisition needs.
• Test equipment: High signal integrity spectrum analyzers, radio frequency generators, and calibrated transform routines are vital for practical verification and device appraisal—ensuring true in-application SFDR and unwanted artifact identification.
• Application notes & support documents:
  • "Dynamic Testing of High-Speed ADCs, Part 1 & 2" (Analog Devices)
  • "Impact of Sampling-Clock Spurs on ADC Performance" (TI Application Report)
  • "A/D Converter Calculations for RF Applications" (RF Cafe)

Key Parameters and Symbols for Spur and SFDR Calculations

Parameter/Symbol	Definition	Typical Units
VFS(pk)	Full-scale peak input voltage	V
VFS(pk-pk)	Full-scale peak-to-peak voltage	V
VFS(rms)	Full-scale input RMS voltage	V
PFS(mW)	Full-scale input power	mW
PFS(dBm)	Full-scale input power in dBm	dBm
fsample	Sampling frequency	Hz
VLSB	Voltage step for 1 LSB	V
SNR	Signal-to-noise ratio	dB
N	Number of bits	bits
NF	Noise Figure	dB
SFDR	Spurious-Free Dynamic Range	dBc
THD	Total Harmonic Distortion	dB
IMD	Intermodulation Distortion	dB
ENOB	Effective Number of Bits	bits

About the Author and Support

Read about the technical expertise behind this tool

Julian Jenkins, CEO and CTO of Perceptia Devices, is a recognized leader in PLL and radio design, with deep experience in the design and evaluation of high-speed analog and a2d ics. Contributions from prominent designers at Analog Devices and industry consultants ensure this remains at the cutting edge of calculators for your bench.

For additional support, expert consultation, or customized tool integration with your workflow, contact our support team.

Conclusion: Using ADC Spurious Calculator Insights for Solution Planning

Understanding spurious signals, noise sources, IMD, and SFDR through real validation and precise calculation enables you to make data-driven design decisions—whether you’re optimizing the chain in a radio platform, verifying spur constraints for robust signal transmission, or developing high-end a2d systems for wireless, digital, or test deployments. The adc spurious calculator delivers transparent, actionable spur analysis for bench-ready projects and real-world product success and ensures you can account for output signal consistency and minimize jitter for the highest rf electrical performance. You might also find our ADC Calculator useful.

What is ADC spurious analysis and why is it important?

ADC spurious analysis identifies unwanted frequency components that appear in the digitized signal due to harmonic distortion and Nyquist aliasing. This is crucial for determining if harmonics of the input signal will fold back into your frequency band of interest, potentially corrupting your measurements.

How does Nyquist aliasing affect ADC performance?

When harmonics of the input signal exceed the Nyquist frequency (half the sampling rate), they fold back or 'alias' into lower frequency ranges. This can cause spurious signals to appear within your desired frequency band, degrading signal quality and measurement accuracy.

What is the relationship between sampling frequency and spurious performance?

Higher sampling frequencies push harmonic aliases further away from the fundamental frequency, improving spurious performance. However, the optimal sampling rate depends on your specific application and the frequency band of interest.

How do I interpret the harmonic analysis results?

The table shows each harmonic order, its original frequency, and where it aliases after sampling. Pay attention to harmonics marked as 'In Band' - these are the ones that will interfere with your signal of interest and may require filtering or different sampling strategies.

What is SFDR in ADC specifications?

Spurious Free Dynamic Range (SFDR) is the ratio between the fundamental signal amplitude and the largest spurious signal amplitude, typically expressed in dB. Higher SFDR values indicate better ADC performance with fewer spurious components.

How can I improve ADC spurious performance?

Use anti-aliasing filters before the ADC, choose appropriate sampling frequencies, ensure clean input signals with low harmonic content, and select ADCs with better linearity specifications. Proper board layout and power supply design also help minimize spurious signals.

What factors determine the maximum harmonic order to analyze?

Typically analyze harmonics up to the 9th order as higher-order harmonics have progressively lower amplitudes. However, for high-performance applications or when using ADCs with poor linearity, you may need to consider higher-order harmonics up to the 20th order.