Cascaded Gain
Understanding Cascaded Gain
Gain Accumulation in RF Signal Chains
In RF transmitters and receivers, a single amplifier stage rarely provides the total gain required to boost a weak signal to the level needed for processing or transmission. Consequently, multiple amplifier stages are placed in series, creating a cascaded gain network. The signal power increases step-by-step as it passes through each successive stage. Managing this gain distribution is a critical aspect of RF design, affecting noise performance, linearity, and power consumption.
For small-signal linear analysis, the total gain is calculated by multiplying the individual gain factors of each stage. When working with decibels (dB), this multiplication simplifies to addition, where the total gain is the sum of the individual gains minus the insertion losses of any passive filters, attenuators, or cables placed between the active stages.
Impedance Mismatch and Gain Ripple
The theoretical calculation of cascaded gain assumes that all stages are perfectly matched to the system characteristic impedance, typically 50 ohms. In reality, every active device has input and output impedances that deviate from 50 ohms and vary over frequency. When these stages are connected, the impedance mismatches cause signal reflections at each interface. These reflections create standing waves, introducing mismatch loss and gain ripple across the operating frequency band. To stabilize cascaded gain, designers place matching networks, attenuator pads, or ferrite isolators between stages to absorb reflections.
Key Mathematical Relations
Technical Specifications Comparison
| Amplifier Stage | Linear Gain (V/V) | Logarithmic Gain (dB) | Cumulative Gain (dB) | Output Power Level (dBm) |
|---|---|---|---|---|
| Input Signal | - | - | 0.0 | -90.0 |
| Stage 1 LNA | 31.6 | +15.0 | 15.0 | -75.0 |
| RF Filter (Loss) | 0.79 | -1.0 | 14.0 | -76.0 |
| Stage 2 Mixer | 0.50 | -6.0 | 8.0 | -82.0 |
| Stage 3 IF Amp | 100.0 | +20.0 | 28.0 | -62.0 |
Frequently Asked Questions
How do you calculate cascaded gain in decibels?
To calculate cascaded gain in decibels, you add the individual gain values of each stage (expressed in dB) and subtract the insertion losses and mismatch losses of any filters, attenuators, or cables located between the stages.
How does impedance mismatch affect the actual cascaded gain?
Impedance mismatch at stage boundaries causes a portion of the RF signal to reflect back toward the source rather than transferring to the next stage. This reflection creates mismatch loss, reducing the overall gain and causing frequency-dependent ripple.
What is gain compression in cascaded amplifiers?
Gain compression occurs when high input signal levels drive one or more amplifiers in the cascade beyond their linear operating regions. The output stages saturate, causing the cumulative gain to drop below the small-signal value, which distorts the signal.