Stopband Attenuation

The minimum attenuation in dB that a filter must provide across the entire stopband. This parameter directly sets the floor for out-of-band emission suppression.

• Typical values: 40-80 dB for SAW/BAW filters, 60-100+ dB for cavity filters
• Design trade-off: Higher A_min requires higher filter order, increasing insertion loss and group delay
• Specification: Defined at worst-case frequency within the stopband, not average
• Impact: Insufficient A_min allows spectral regrowth products to leak into adjacent channels, violating ACLR limits

The frequency boundary separating the transition band from the stopband. Beyond this edge, attenuation must meet or exceed the specified minimum.

• Placement: Typically set at the adjacent channel boundary plus guard band margin
• Relationship: Closer f_s to passband edge requires sharper roll-off, increasing filter complexity
• System impact: Determines how much spectrum is sacrificed to filtering versus usable bandwidth
• Design rule: f_s is often placed at 1.5-2x the passband edge frequency for realizable filters

The number of reactive elements (poles) in a filter transfer function, determining the transition band steepness in dB/octave or dB/decade.

• Roll-off rate: Each filter order contributes approximately 20 dB/decade (6 dB/octave) of attenuation slope
• Butterworth: Maximally flat passband, moderate roll-off (20n dB/decade for order n)
• Chebyshev: Faster roll-off with passband ripple trade-off
• Elliptic (Cauer): Steepest roll-off for given order, with stopband ripple
• Practical limit: Higher order increases insertion loss, group delay variation, and physical size

The frequency gap between the passband edge (f_p) and stopband edge (f_s). Narrower transitions demand higher filter orders or more complex topologies.

• Transition ratio: Defined as f_s / f_p; values near 1.0 indicate extremely sharp filters
• Guard band allocation: Transition width consumes spectrum that cannot be used for signal transmission
• DPD feedback path: Wide transition bandwidth simplifies anti-aliasing filter design before ADC
• Typical ratios: 1.1-1.3 for practical RF filters, <1.05 for high-performance crystal/SAW filters

The peak-to-peak variation of attenuation within the stopband. While passband ripple affects signal fidelity, stopband ripple determines worst-case adjacent channel leakage.

• Elliptic filters: Exhibit equiripple behavior in both passband and stopband
• Specification: Minimum stopband attenuation must account for ripple troughs, not peaks
• Critical frequency: Worst-case rejection occurs at ripple minima, potentially allowing spectral regrowth spikes
• Mitigation: Over-design A_min by 6-10 dB to account for manufacturing tolerances and temperature drift

Environmental and production variations that degrade stopband attenuation from nominal design values, requiring margin allocation.

• Temperature drift: SAW/BAW filters shift 20-50 ppm/°C, cavity filters shift with thermal expansion
• Aging effects: Crystal and ceramic filters experience long-term frequency drift
• Production tolerance: Typical ±0.5-2% center frequency variation in volume manufacturing
• Design margin: Allocate 5-10 dB additional stopband attenuation to maintain compliance across operating temperature range (-40°C to +85°C)

The primary regulatory metric for spectral regrowth, quantifying the ratio of in-channel power to power leaking into adjacent channels.

• Measurement: Integrated power in assigned channel vs. power in offset adjacent channels
• Typical Requirements: -45 dBc for 3GPP LTE/5G NR adjacent channel; stricter for narrowband offsets
• Relationship: Directly determined by stopband attenuation of the transmitter's effective filtering and linearization
• Testing: Measured with modulated test signals at maximum rated power

A regulatory-defined power spectral density envelope that sets absolute emission limits across frequency offsets, not just adjacent channels.

• Definition: Maximum allowed PSD at each frequency offset from the carrier
• Enforcement: FCC, ETSI, and 3GPP specify masks for each radio standard
• Stopband Role: The stopband attenuation of transmitter filtering must ensure emissions remain below the mask at all offsets
• Critical Regions: Close-in offsets (0-5 MHz) dominated by PA nonlinearity; far-out offsets by noise floor

Nonlinear products generated at sum and difference frequencies when multiple signals pass through a nonlinear device.

• IMD3: Third-order products at 2f₁-f₂ and 2f₂-f₁, falling closest to the original carriers and causing adjacent channel interference
• IMD5/IMD7: Higher-order products that fall further from carriers but contribute to far-out spectral regrowth
• Suppression: Requires high stopband attenuation in the linearization system to cancel these products
• Two-Tone Test: Classic characterization method using two CW tones to measure IMD levels

The two fundamental nonlinear mechanisms in power amplifiers that generate spectral regrowth.

• AM-AM: Amplitude-to-amplitude nonlinearity causing gain compression at high envelope levels
• AM-PM: Amplitude-to-phase conversion where phase shift varies with instantaneous envelope power
• Spectral Impact: AM-AM creates symmetric spectral regrowth; AM-PM creates asymmetry in upper and lower sidebands
• DPD Correction: Digital predistortion must independently model and invert both AM-AM and AM-PM characteristics

PA behavior where current output depends on past input states due to thermal, electrical, and trapping dynamics.

• Thermal Memory: Slow time constants (microseconds to milliseconds) from die heating and cooling
• Electrical Memory: Fast time constants from bias network impedance variations and envelope frequency-dependent effects
• Impact on Stopband: Memory effects create frequency-dependent nonlinearity that limits achievable stopband attenuation
• Modeling: Requires Volterra series or memory polynomial models with sufficient memory depth

Signal conditioning that reduces peak-to-average power ratio before amplification, enabling higher average power without clipping-induced spectral regrowth.

• Hard Clipping: Simple amplitude limiting but generates severe out-of-band emissions
• Peak Windowing: Applies smooth windowing function to peaks for better spectral containment
• Pulse Injection: Cancels peaks with shaped pulses that minimally impact EVM
• Synergy with DPD: CFR and digital predistortion work together—CFR reduces peak demands while DPD linearizes the remaining signal path