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The Friis formula for cascaded noise figure:

(All values in linear, not dB.) The first stage dominates the overall noise figure because subsequent stage contributions are divided by the cumulative gain of preceding stages.

A typical superheterodyne transceiver includes:

• Antenna: Converts EM waves to/from electrical signals
• Duplexer/Switch: Separates TX and RX paths
• Band-pass Filter: Selects desired band, rejects out-of-band
• LNA (RX): Amplifies weak signal with minimal noise addition
• Mixer + LO: Frequency translation to/from IF
• IF Filter & Amplifier: Channel selection and gain
• ADC/DAC: Digital-to-analog conversion interface
• PA (TX): Power amplification for transmission
• Frequency Synthesizer (PLL): Generates precise LO frequencies

The LNA (first gain stage in the RX chain) is the most critical. Per the Friis formula, the first stage’s noise figure adds directly to the system NF, while all subsequent stages are divided by the preceding gain. A high-gain, low-NF LNA suppresses the noise contribution of everything downstream.

The LNA amplifies the input noise by its gain AND adds its own noise:

The signal is amplified by 10dB (gain only). If the signal input was −80dBm, it becomes −70dBm at output. The SNR degrades by the NF (2dB): from 20dB input SNR to 18dB output SNR.

A PLL-based synthesizer noise profile:

• Reference oscillator: Dominates close-in phase noise (very low offsets). Multiplied by N² when transferred to the output.
• Phase detector / Charge pump: Contributes flat noise within the loop bandwidth, multiplied up to the output.
• Loop filter: Shapes the transition between in-band and out-of-band noise.
• VCO: Dominates outside the loop bandwidth with a −20dB/decade slope (or −30dB/decade with 1/f noise).

Inside the loop bandwidth → reference and PFD/CP noise dominate. Outside the loop bandwidth → VCO’s free-running phase noise dominates.

In QPSK, both I and Q channels transition simultaneously, allowing 180° phase jumps which cause the signal envelope to pass through zero — problematic for nonlinear amplifiers.

In OQPSK (Offset QPSK), the Q channel is delayed by half a symbol period, so I and Q never transition at the same time. This limits maximum phase change to 90°, preventing envelope zero-crossings and reducing spectral regrowth through nonlinear PAs.

Compression (AM-AM distortion) causes the outer constellation points to be pushed inward, because the amplifier saturates and delivers less gain at higher amplitudes. Additionally, AM-PM conversion rotates constellation points. For QPSK, since all four symbols have equal amplitude, compression uniformly reduces the constellation radius and may add a phase offset. The EVM increases and the four points cluster closer together, reducing noise margin.

Phase noise causes random rotation of the entire constellation around the origin. Each constellation point spreads into an arc. For 16QAM, the outer points (higher amplitude) are affected more severely because the arc length is proportional to the radius. This increases EVM and can cause symbol errors, especially between adjacent symbols in the angular direction. Integrated phase noise directly limits the achievable modulation order.

Techniques include:

• Digital Pre-Distortion (DPD): Apply the inverse of the PA’s nonlinear transfer function in the digital domain before the DAC.
• Envelope Tracking (ET): Dynamically adjust the PA supply voltage to follow the signal envelope, keeping the PA near saturation while maintaining linearity.
• Doherty PA: Uses a main and peaking amplifier to maintain efficiency across a range of output power levels.
• PAPR Reduction: Crest Factor Reduction (CFR) techniques to clip or reshape peaks before amplification.

Before the PA: A BPF may be needed to reject out-of-band noise from the upconversion chain (LO leakage, image, synthesizer spurs) that could be amplified by the PA and violate spectral emission masks.

After the PA: A BPF is typically required to suppress harmonics and intermodulation products generated by the PA’s nonlinearity. Considerations include: insertion loss (directly reduces output power and efficiency), power handling capability, filter order vs. rejection requirements, and whether the PA’s harmonic levels already meet regulatory emission masks without filtering.

An ideal rectangular pulse in the time domain has a sinc function spectrum in the frequency domain, which extends to infinity. When filtered (band-limited), the pulse loses high-frequency components and becomes distorted (ringing, ISI).

Solution: Pulse shaping. Use a sinc-shaped pulse (or practical approximations like raised-cosine) in the time domain, which produces a band-limited rectangular spectrum. This confines the signal bandwidth while maintaining zero-ISI at sampling instants.

For two input tones at f₁ and f₂, the 3rd-order intermodulation products (IM3) appear at:

These are problematic because they fall close to the original tones (in-band) and cannot be easily filtered out.

IM3 products follow a 3:1 slope relative to input power. If both tones decrease by 1dB, the IM3 products decrease by 3dB.

The IM3 product at 2f₁−f₂ depends on f₁²·f₂, so if f₁ is reduced by 1dB, this product drops by 2dB. The product at 2f₂−f₁ depends on f₂²·f₁, so it drops by 1dB.

In general, the IM3 product that is “closer” to the reduced tone drops by 2dB, and the one closer to the other tone drops by 1dB.

To verify that observed distortion products are from the DUT and not the spectrum analyzer:

• Add external attenuation (e.g., 10dB pad) at the SA input. If IM products drop by more than the attenuation amount (3:1 for IM3), they were generated inside the SA.
• Reduce the SA’s input mixer level by increasing internal attenuation.
• Check the SA’s specified TOI and ensure input levels are well below it.
• Compare results at different SA attenuation settings — DUT-generated products remain constant relative to the fundamental.

For most well-behaved amplifiers, the input IP3 (IIP3) is approximately 9.6dB above the input 1dB compression point (P1dB):

This is a rule of thumb assuming a 3rd-order polynomial model. Real devices may deviate from this relationship.

PIM (Passive Intermodulation) is the generation of intermodulation products by passive components (connectors, cables, junctions of dissimilar metals). “Low-PIM” means the component or system generates minimal passive IM distortion, which is critical in multi-carrier base station environments where PIM products can fall into receive bands and degrade sensitivity. Typical low-PIM specs are ≤ −153dBc.

The last stage (closest to the output) typically dominates cascaded IIP3, because it sees the highest signal levels:

(All linear.) Each stage’s contribution is amplified by the gain of all preceding stages. This is opposite to noise figure, where the first stage dominates.

1. Verify test setup: Calibrate cables, check connectors, confirm signal generator accuracy.
2. Measure noise floor: Terminate the antenna port and measure the RX noise floor — compare to expected kTB + NF + Gain.
3. Stage-by-stage analysis: Inject signals at intermediate points to isolate which stage has degraded gain or elevated NF.
4. Check for interference: Look for spurs, LO leakage, or self-generated interference raising the noise floor.
5. Check for compression: Ensure no stage is being overdriven by a strong blocker, causing desensitization.
6. Inspect hardware: Check solder joints, component values, bias points, and power supply noise.

• PA compression: Operating too close to saturation, generating spectral regrowth.
• DPD malfunction: Digital pre-distortion not converging or miscalibrated.
• Phase noise: Excessive LO phase noise spreading energy into adjacent channels.
• DAC nonlinearity or clipping: Insufficient DAC backoff or resolution.
• Baseband filtering: Inadequate pulse shaping or digital filtering.
• Power supply noise: Supply modulation coupling into the PA or mixer.

The signal and noise add in power (not in dB):

P_signal = 10^(−9.0) mW, P_noise = 10^(−10.0) mW

P_total = 10^(−9) + 10^(−10) = 1.1 × 10^(−9) mW = −89.6 dBm

The reading is approximately −89.6dBm — about 0.4dB above the true signal level.

A common LNA topology is the common-source (or common-emitter) with inductive degeneration. The transistor provides gain, the inductive source degeneration creates a real part in the input impedance for matching without adding thermal noise (unlike a resistor), and a cascode transistor may be added to improve reverse isolation and increase output impedance.

LNA input matching involves two goals: impedance match (for maximum power transfer, typically 50Ω) and noise match (for minimum noise figure, matching to Z_opt). These two impedances are generally different. Common techniques:

• Inductive source degeneration to create a real impedance component
• Input series inductor (gate inductor) to resonate out the gate capacitance
• Simultaneous noise and impedance matching (SNIM) techniques

A degeneration inductor is placed at the source (or emitter) of an LNA transistor. Its roles:

• Creates a real component in the input impedance: Re(Z_in) = g_m·L_s/C_gs, enabling 50Ω matching without a lossy resistor
• Improves linearity through negative feedback
• Provides stability by reducing gain at all frequencies
• Does not add thermal noise (unlike resistive degeneration), preserving low NF

• Class A: Transistor conducts 100% of cycle. Most linear, lowest efficiency (~50% max theoretical).
• Class B: Conducts 50% of cycle. Better efficiency (~78.5%), less linear.
• Class AB: Conducts 50–100%. Practical compromise between linearity and efficiency.
• Class C: Conducts <50%. High efficiency, very nonlinear — used for constant-envelope signals.
• Class D/E/F: Switching amplifier classes. Transistor acts as a switch, achieving very high efficiency (>90%). Class E uses zero-voltage switching; Class F uses harmonic tuning.

Drain/Collector Efficiency:

Power Added Efficiency (PAE):

PAE accounts for the input drive power, making it a more meaningful metric, especially for low-gain amplifiers. For high-gain PAs, PAE ≈ drain efficiency.

Per the Friis noise figure formula, the first stage’s noise figure dominates the overall system noise figure, because all subsequent stage noise contributions are divided by the preceding gain. By placing a high-gain, low-NF LNA first, the weak received signal is amplified before encountering noisier stages (mixers, filters), minimizing their noise contribution and maximizing receiver sensitivity.

This is a trick question. In the Friis equation, the (λ/4πd)² term becomes greater than 1 when d < λ/4π. However, the Friis equation is a far-field approximation and is not valid at such short distances (near field). In the near field, the simple free-space path loss model breaks down. Conservation of energy tells us you can’t create power from nothing.