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Cascaded Amplifier Gain, Noise Figures, and Distortion

Guitar cascaded amplifier gain

Don’t try to daisy chain your guitar amplifier to get more cascaded amplifier gain


When I used to play guitar, I quickly realized the last thing you should do is connect your amplifiers together. I’ve always been into rock music and love the distortion in guitar, but chaining guitar amplifiers only make the sound worse. In your electronic circuits, you can daisy chain your amplifiers into a cascaded amplifier to increase an input signal to a higher level at the output.

With any multistage amplifier, there is a question of the cascaded amplifier gain and saturation points that can be reached in these circuits without producing distortion. In addition, noise at the input can be propagated to the output, where it also experiences gain. Here’s how a cascaded amplifier provides gain while operating in the linear range and how to configure your amplifier stages to prevent distortion.

What is a Cascaded Amplifier?

When some designers hear the word “amplifier,” they probably think of op-amps. These components are packaged in individual ICs and have the familiar triangular symbol in a circuit diagram or schematic. Real amplifiers for specialized applications don’t always contain a single amplifier circuit. Instead, they are cascaded amplifiers. A cascaded amplifier simply means multiple amplifiers lumped together into a single device. The output of one amplifier stage is connected to the input amplifier stage. It is not uncommon to see four amplifier stages in specialized amplifier ICs. Some examples include laser pulse driver amplifiers, and power amplifiers for RF designs.

Placing the amplifier stages in series in this way allows more gain to be applied to an input signal. The gain provided by each stage of the amplifier is additive or multiplicative, as long as each stage of the amplifier is not running in the saturation regime. An example of a 2-stage common emitter amplifier circuit is shown in the circuit diagram below.


Cascaded amplifier gain with 2 stages

2-stage common emitter amplifier


In the above schematic, the common emitter configuration for an NPN transistor has been used for the amplifier stages, but you could also use the common collector configuration. Other configurations use MOSFET amplifier stages, particularly power amplifiers. The configuration of resistors (and capacitors/inductors) will determine the gain of an individual amplifier stage. However, the total cascaded amplifier gain will depend on the gains from the individual amplifiers.

Cascaded Amplifier Gain and Noise Figure

The gain of an amplifier section is just the output signal divided by the input. Since the output voltage from one stage is the input to the next stage, the total gain is the product of gains from each amplifier stage:


Cascaded amplifier gain equation


Note that gain could also be calculated in terms of input and output current. In dB terms, the total gain is just the sum of dB gains from each amplifier stage:


Cascaded amplifier gain in dB


Any noise that is present on the input signal will also be amplified. The total noise produced at the output of the amplifier is shown in the equation below. Note that this signal is a standard noise figure and is expressed as a voltage in dB. Each Gi and Ni value is expressed in dB, and n0 is the input noise level in dB.


Cascaded amplifier gain seen by noise in dB


Note that these equations assume the amplifier is operating in the linear regime. If the input signal in an amplifier stage is too large and the amplifier saturates, the output signal from that stage will stop increasing. However, the noise level will be low enough that the noise will still continue acquiring gain and increasing. In order to prevent noise from increasing faster than the signal level, each amplifier stage must run in the linear regime.

Discrete Multistage Amplifiers

If you’re innovating a new component architecture for a specific application, and an SoC or ideal IC is not available, you can build your own multistage amplifiers from separate single-stage amplifier ICs. This is a good way to experiment with new cascaded amplifier chains before designing an SoM, SoC, or multistage amplifier IC.

The key point to consider when designing a custom cascaded amplifier chain is to determine the saturation point for each of the amplifier stages. The gain provided by an amplifier stage can only be realized when the amplifier runs in the linear regime. If one amplifier stage is running near saturation, all subsequent stages can saturate, leading to strong clipping and harmonic generation in the output signal.

Just like an individual transistor, the linear regime for a particular amplifier stage can be determined from a load line simulation. This essentially involves performing a series of DC sweeps for the amplifier input voltage. The output from one stage becomes the input to the next stage; depending on the values of the resistors connected to each stage (see resistors R1 and R3 above), the load line for a subsequent stage may lie in the saturation region. This should be checked during design.


 Load line for a power amplifier

Load line for a cascaded amplifier.


Whether you’re designing a custom multistage amplifier for a specialized signal chain, or you need to simulate cascaded amplifier gain and efficiency, you’ll need the right set of PCB layout and design software. Allegro PCB Designer and Cadence’s full suite of design tools can help you create your cascaded amplifier from verified component models and analyze all aspects of its functionality. You’ll also have access to a set of tools for MCAD design and preparing for manufacturing.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.