Power Supply Rejection Ratio

In the world of electronics, sensitive circuits must amplify faint, important signals while being powered by sources that are often noisy and imperfect. The ability of a circuit to ignore this electrical "chatter" on its power supply is a critical measure of its performance. This capability is quantified by the Power Supply Rejection Ratio (PSRR), a figure of merit that defines a component's immunity to power supply noise. Understanding PSRR is essential for designing robust, high-performance systems, yet the mechanisms behind it and its far-reaching consequences are often overlooked. This article bridges that gap by providing a clear and detailed exploration of this fundamental concept.

The following chapters will guide you through the intricacies of PSRR. First, the "Principles and Mechanisms" section will break down what PSRR is, how it is measured, and where it originates—from physical imperfections in transistors to the corrective power of negative feedback. We will also explore its critical dependence on frequency. Subsequently, the "Applications and Interdisciplinary Connections" section will demonstrate the real-world impact of PSRR, showing how it dictates the performance of essential components like operational amplifiers, voltage regulators, and data converters, ultimately determining the integrity of complex electronic systems.

Imagine you are trying to listen to a faint whisper in a noisy room. Your brain does a remarkable job of filtering out the background chatter so you can focus on the quiet voice. In the world of electronics, amplifiers often face a similar challenge. They are designed to listen to and amplify very small, important signals—the electrical equivalent of a whisper. But the power they draw from the wall or a battery is almost never perfectly clean; it's often contaminated with noise, ripple, and fluctuations—the electrical equivalent of background chatter. An electronic circuit's ability to ignore this "chatter" on its power supply and focus only on the intended signal is one of its most critical virtues. This virtue is quantified by a figure of merit called the ​​Power Supply Rejection Ratio​​, or ​​PSRR​​.

At its core, PSRR is simply a ratio: How big is the noise on the power supply line compared to the noise that actually makes it through to the component's output? A higher PSRR means the component is better at rejecting, or attenuating, this unwanted supply noise.

Because this rejection can be extraordinarily effective, engineers use a logarithmic scale called decibels (dB) to express it. The relationship is given by $PSRR_{dB} = 20 \log_{10}(\frac{\Delta V_{supply}}{\Delta V_{out}})$, where $\Delta V_{supply}$ is the variation on the power supply and $\Delta V_{out}$ is the resulting variation on the component's output. The logarithmic scale is convenient because our minds are not well-equipped to grasp the difference between a rejection of 10,000-to-1 and 100,000-to-1, but the difference between 80 dB and 100 dB is more intuitive to an engineer.

Let's make this tangible. Consider a common voltage regulator, the LM7805, whose job is to provide a stable 5-volt output. Suppose it's fed by a power source that has a 1.5-volt peak-to-peak ripple—a fairly messy supply. The datasheet might specify a PSRR of 78 dB. What does this mean for our circuit? Plugging this into the formula, we find that the rejection ratio is $10^{(78/20)}$, which is approximately 7943. This means the regulator suppresses the incoming ripple by a factor of nearly 8000! The nasty 1.5 V ripple at the input is crushed down to a minuscule ripple of only about 0.189 millivolts ($mV$) at the output. The regulator acts like an incredibly effective set of noise-canceling headphones for your circuit.

How does this rejection actually happen? It's tempting to think of supply noise as something that just "leaks" directly to the output. But the mechanism is more subtle and much more interesting. Variations on the power supply don't just add noise at the end of the line; they create a tiny, phantom error signal right at the most sensitive part of the amplifier: its input.

Imagine an operational amplifier (op-amp) in a sensitive medical device, like an ECG measuring the tiny electrical signals from the heart. The op-amp is powered by a battery. As the battery discharges, its voltage drops. The op-amp's internal circuitry is not perfectly insensitive to this drop. The change in supply voltage slightly alters the operating points of the transistors inside, creating a small imbalance that the amplifier interprets as a change in the input signal. This phantom signal is called the ​​input-referred offset voltage change​​.

The PSRR, in this context, is defined as the ratio of the change in supply voltage to the equivalent input offset voltage it creates: $PSRR = \frac{\Delta V_{supply}}{\Delta V_{os}}$. An op-amp with a high PSRR is one where even a large swing in the supply voltage produces an almost insignificant phantom signal at its input. For an ECG, this is critical. A drop in battery voltage should not look like a change in the patient's heartbeat! For a precision op-amp with a PSRR of 92 dB, a battery drop from 4.2 V to 3.6 V (a 0.6 V change) would only generate an equivalent input error of about 15 microvolts ($\mu V$). The op-amp is so good at rejecting the supply change that the "ghost" it creates is almost immeasurably small.

This concept of input-referred noise is powerful because it allows us to separate the amplifier's two main jobs: rejecting noise and amplifying signals. First, the PSRR tells us how much of the supply noise gets converted into a tiny phantom signal at the input. Then, this tiny phantom signal is amplified by the circuit's overall gain, just like the real signal we care about.

This is where things can get tricky. If you have a high-gain amplifier, even a minuscule input-referred noise can become a significant problem at the output. Consider a system where a 40 mV ripple on the power supply needs to be rejected. An op-amp with a PSRR of 92 dB will convert this into an input-referred noise of just about 1 $\mu V$. A whisper. But if this op-amp is in a circuit with a voltage gain of 120, this 1 $\mu V$ whisper is amplified to a 0.121 mV roar at the output. This highlights a fundamental trade-off in amplifier design: high gain, which is often desirable, will also amplify any residual noise that the PSRR couldn't eliminate.

It's also important here to distinguish PSRR from its cousin, the Common-Mode Rejection Ratio (CMRR). While PSRR measures the rejection of noise from the power lines, CMRR measures the rejection of noise that appears identically on both input terminals of a differential amplifier (like 60 Hz hum picked up by sensor wires). Both create unwanted signals, but they originate from different places and are rejected by different internal mechanisms.

Why isn't PSRR infinite? Why does any supply noise get through at all? The answer lies in a fundamental principle of design: symmetry. The input stage of most op-amps is a ​​differential pair​​—two carefully matched transistors working in tandem.

In a perfect world, if a change occurs on the power supply, it affects both transistors and their surrounding components in exactly the same way. When we take the differential output (the difference between the two halves), this common disturbance cancels out perfectly, and no noise gets through. The PSRR would be infinite.

But we don't live in a perfect world. During fabrication, it's impossible to make two transistors and two resistors absolutely identical. There will always be a tiny ​​mismatch​​. Let's say one load resistor is $R_C$ and the other is $R_C + \Delta R$. Now, when the supply voltage changes, it causes a slightly different effect on each side of the pair. The cancellation is no longer perfect. A small part of the supply disturbance "leaks" through as a differential signal. The size of this leakage is directly related to the mismatch, $\Delta R$. The formula derived from analyzing this circuit, $PSRR^{+} = -\frac{g_{m}}{g_{ps}}\cdot\frac{2R_{C}+\Delta R}{\Delta R}$, reveals this beautifully. As the mismatch $\Delta R$ approaches zero, the PSRR approaches infinity. The quest for high PSRR is, at its heart, a quest for perfect symmetry within the silicon chip.

Another path for supply noise comes from a transistor property called the ​​Early effect​​, which gives the transistor a finite output resistance, $r_o$. This resistance effectively creates a voltage divider between the power supply and the output, providing a direct path for noise to leak through. Interestingly, the gain of the amplifier stage, which is proportional to its transconductance $g_m$ and load resistance $R_C$, helps fight this leakage. The PSRR for a simple common-emitter stage turns out to be proportional to $g_m r_o$. This implies that a higher-gain transistor stage is inherently better at rejecting supply noise from this particular path.

So, the "raw" open-loop PSRR of an op-amp is limited by these physical imperfections. How do we build circuits that have truly phenomenal noise rejection? The answer is one of the most powerful concepts in all of engineering: ​​negative feedback​​.

By wrapping a feedback loop around the op-amp (for example, in a standard non-inverting amplifier configuration), we create a self-correcting system. The feedback network continuously monitors the output and compares it to the desired input. If a fluctuation from the power supply tries to push the output voltage up or down, the feedback loop instantly senses this deviation and instructs the op-amp to counteract it.

The effectiveness of this correction is determined by the ​​loop gain​​, a quantity given by $1 + \beta A_{OL}$, where $A_{OL}$ is the op-amp's massive open-loop gain and $\beta$ is the fraction of the output that is fed back. The result is that the closed-loop PSRR is improved by this exact factor. For instance, an op-amp with a respectable open-loop PSRR of 80 dB ($10,000:1$) and an open-loop gain of $1.25 \times 10^{5}$, when placed in a circuit with a feedback configuration that gives it a closed-loop gain of 25, will see its PSRR boosted by a factor of about 5000. The final closed-loop PSRR becomes a staggering 154 dB, which is a rejection ratio of over 50 million to one! Negative feedback takes the good raw performance of the op-amp and elevates it to near perfection.

There is, however, one final catch. An amplifier's PSRR is not constant across all frequencies. The internal circuitry of an op-amp, like anything in the physical world, cannot respond instantaneously. As the frequency of the supply noise increases, the amplifier's ability to reject it begins to fall off.

This is a critical limitation in the real world, where noise is often not a simple DC offset but a complex mix of frequencies, from the 120 Hz hum from power supplies to high-frequency switching noise from digital logic. The PSRR of an op-amp might be a stellar 100 dB at DC, but it will start to roll off, often beginning at a relatively low frequency like 150 Hz. At a noise frequency of 30 kHz, that 100 dB PSRR might have degraded significantly. This means that a 200 mV, 30 kHz noise signal on the power line, which would be completely obliterated at DC, could now leak through and create a measurable 4 mV noise signal at the amplifier's output. Understanding the frequency-dependent nature of PSRR is crucial for designing robust circuits that work in noisy environments.

Since an amplifier's internal PSRR falters at high frequencies, engineers employ a simple but powerful external tool: the ​​bypass capacitor​​. Imagine the long, thin copper traces on a circuit board that deliver power to an amplifier chip. These traces have some small resistance and inductance. A bypass capacitor is a small capacitor placed right at the power and ground pins of the amplifier chip.

This capacitor acts like a tiny, local reservoir of charge. For steady DC current, the capacitor does nothing. But for high-frequency noise currents, the capacitor provides a very low-impedance path directly to ground. Instead of trying to force its way into the amplifier chip, the high-frequency noise is "bypassed" to ground. This forms a simple RC low-pass filter with the trace resistance, which pre-filters the power supply before it even gets to the amplifier. This simple, inexpensive component is an unsung hero, working hand-in-hand with the amplifier's internal PSRR to ensure that the delicate signal we care about is the only thing the amplifier hears.

In the sanitized world of our circuit diagrams, power supplies are perfect, unwavering sources of pure DC voltage. They are the silent, steadfast foundation upon which we build our electronic castles. But reality, as it so often is, is a far noisier affair. The very act of powering a complex circuit—with digital clocks switching billions of times a second, with motors starting and stopping—creates a storm on the power lines. Voltages surge, dip, and ripple. In this turbulent environment, how can a sensitive circuit possibly do its job? How can a precision instrument measure a faint signal, or a stereo amplifier reproduce music without a hum?

The answer lies in a concept we've already explored: the Power Supply Rejection Ratio, or PSRR. But PSRR is more than just a specification on a datasheet; it's a measure of a circuit's quiet defiance. It is the art of building a calm room in the middle of a hurricane. Let's embark on a journey to see how this crucial property manifests itself, from the very heart of a single transistor to the grand performance of the systems that shape our modern world.

PSRR isn't some magical property bestowed upon a circuit; it is born from the fundamental physics of the components themselves. Let's look under the hood, starting with the workhorse of modern electronics: the transistor. It's as if the transistor has two jobs: its main job is to amplify the input signal, but its side job is to ignore the chattering from its power source. And wonderfully, it turns out that being good at the first job makes it good at the second! When we analyze a simple transistor amplifier like a source follower, we find a beautiful piece of economy from nature. Its ability to reject supply noise is directly related to its own intrinsic gain, the very property that makes it a powerful amplifier in the first place.

But our circuits don't just run on voltage; they are animated by currents. Imagine trying to paint a masterpiece with a brush whose bristles are constantly changing length. This is the challenge faced by designers of current sources. A current mirror, a fundamental building block in nearly every integrated circuit, is designed to create a precise copy of a current. But if the supply voltage wobbles, will the copied current remain true? Analyzing the mirror reveals that its ability to reject supply noise depends on its own internal resistances and transconductance. This shows that the battle for stability must be fought at every level, for every kind of signal, be it voltage or current.

If the inherent PSRR of a transistor is its natural shield, then negative feedback is a powerful force field generator. It is one of the most profound and versatile concepts in all of engineering, and its effect on PSRR is nothing short of magical. Consider an amplifier with a modest ability to reject supply noise. By itself, it might let a small hum or buzz sneak through. But now, let's wrap a simple feedback loop around it. We take a fraction of the output and "show" it to the input. The amplifier now doesn't just amplify a signal; it actively works to keep the output exactly where the input commands it to be.

If a ripple from the power supply tries to nudge the output voltage up, the feedback loop immediately senses this unauthorized change and instructs the amplifier to pull it back down. The result? The amplifier's effective PSRR is magnified by a colossal factor, a factor we call the "loop gain," which is the product of the amplifier's gain $A$ and the feedback factor $\beta$. The improved PSRR becomes $PSRR_{o}(1+A\beta)$, where $PSRR_o$ is the original open-loop PSRR. This loop gain can often be in the thousands or millions! This single, elegant principle is what allows us to build amplifiers of astonishing stability and precision from imperfect, real-world components.

Armed with the power of feedback, let's look at some of the indispensable tools in the electronics designer's kit.

The operational amplifier, or op-amp, is the Swiss Army knife of analog design. In its simplest configuration, the voltage follower, it's supposed to create a perfect copy of an input voltage. But what happens when its power supply is noisy? The op-amp's PSRR tells us exactly how much of that supply noise will bleed through to its output. A PSRR of 80.0 dB, which sounds impressive, means that the supply noise is suppressed by a factor of $10^{4}$. So, a 200.0 mV ripple on the supply might become a mere 0.0200 mV ripple on the output—a tiny ghost of the original disturbance, but a ghost nonetheless, one that could be critical in a high-precision application.

What happens when we use an op-amp not to copy a signal, but to make a decision? A comparator tells us whether one voltage is higher or lower than another. Its "trip point" is the critical threshold where its output flips from "low" to "high." We expect this threshold to be rock-solid. But again, the pesky supply noise interferes. A finite PSRR means the supply ripple effectively makes the trip point jitter back and forth. The comparator becomes indecisive! This jitter might not matter if you're just checking if a battery is low, but if you're trying to precisely time an event in a high-speed system, this uncertainty introduced by the power supply can be a fatal flaw.

Some circuits are designed with PSRR as their very reason for being. A Low-Dropout (LDO) regulator is a guardian, a gatekeeper standing between a noisy power source—like a raw battery or a chaotic switching converter—and the sensitive circuits that need pristine power. Its job is to take a messy input voltage and produce a serenely stable output. Its PSRR is its defining feature. A typical LDO might boast a PSRR of 62 dB, meaning it can reduce a 150 mV ripple from a switching converter down to a whisper-quiet 119 µV. However, this battle is not fought equally on all fronts. PSRR is almost always frequency-dependent, typically getting weaker as the noise frequency increases. So, to truly understand the cleanliness of the final output, engineers must consider the entire spectrum of the input noise and how the LDO's rejection capability changes at each frequency, combining the residual ripple components to find the total noise that gets through.

Deep within the silicon heart of a microprocessor or a precision converter lies a circuit of supreme importance: the bandgap voltage reference. This is the ultimate standard, the "meter stick" of voltage against which all other on-chip voltages are measured. It must be steadfast against changes in temperature and, crucially, variations in the power supply. The overall performance metric for this is called "line regulation"—how much the reference voltage changes for a given change in supply. And when we look closely at what determines this line regulation, we find our old friend, PSRR, at the core. The stability of the entire reference circuit often boils down to the PSRR of the op-amp used in its feedback loop. A flaw in the op-amp's ability to reject supply noise directly translates into a flaw in the chip's fundamental voltage standard, a beautiful and direct link from component specification to system-level integrity.

In the end, we don't care about PSRR for its own sake. We care about what it allows us to do. The final test is always the performance of the complete system, connecting the analog world to the digital realm of data, information, and control.

Consider a Digital-to-Analog Converter (DAC), a device that translates abstract digital ones and zeros into a real-world analog voltage. It's an artist painting a picture with voltage levels. If the DAC's power supply is noisy, its PSRR determines how much of that noise contaminates the final artwork. A PSRR of -60 dB means a 100 mV ripple on the power line will superimpose a 0.100 mV noise signal on top of the beautiful waveform the DAC is trying to generate. In high-fidelity audio or precision instrumentation, this is the difference between a clean signal and one corrupted by hum and distortion.

Perhaps the most direct consequence is seen in an Analog-to-Digital Converter (ADC), the gateway from the physical world to the digital realm. An ADC's quality is measured by its Signal-to-Noise and Distortion Ratio (SINAD), a measure of the purity of its conversion. Even if you have an ADC that is intrinsically almost perfect, powering it from a noisy supply can compromise its performance. The supply ripple, attenuated by the ADC's PSRR, appears as an extra noise source at the input. This new noise adds to the ADC's own internal noise, and the result is a tangible degradation of the final measurement quality. In one scenario, an excellent intrinsic SINAD of 82.0 dB could drop to an effective 81.9 dB due to a modest ripple on the supply. This may seem like a tiny drop, but in the world of high-precision science and metrology, where every fraction of a decibel counts, it can be the difference between a discovery and a failed experiment.

So, we see that the Power Supply Rejection Ratio is far from an arcane detail. It is a golden thread that ties together the physics of a transistor, the elegant mathematics of feedback loops, the design of critical building blocks like op-amps and regulators, and the ultimate performance of the complex systems we rely on. It represents a constant, vigilant struggle against the chaos of the real world. Understanding PSRR is understanding that in electronics, as in so much of life, true strength is not just about the power you wield, but also about the noise you can ignore.