# What Is the Relationship Between Analog Bandwidth and Rise Time Lasers are precise pieces of technology and integral to many different scientific and engineering applications. Many laser applications require the modulation of the current signal to control the optical output, often using square or sine waves. The speed, or frequency, of these changes is important when defining the requirements of the control system. Continue reading to learn more about the relationship between analog bandwidth and rise time.

## What Is Bandwidth?

The first step to understanding the relationship between rise time and analog bandwidth is understanding bandwidth. Analog bandwidth, or 3 dB bandwidth, measures the electrical frequency range a system can support. The system will attenuate the input signal frequency. Components outside the 3dB bandwidth are strongly attenuated.

To measure a system’s 3 dB bandwidth, you typically use a sine wave as an input signal and determine the point at which the amplitude of the sine wave decreases by 3dB (1/) from a reference sine wave. Typically, you’ll use a reference value corresponding to the lowest oscillation frequency input signal, usually several orders or magnitude lower than the bandwidth frequency.

## What Is Rise Time?

Rise time is the time between two points on a signal’s rising edge, usually specified as the transition time for a signal to go from the 10% to the 90% level of the steady maximum value.

They describe the fastest response your system can make to a change in the input signal. You can calculate the minimum rise time for a system by measuring the jump from a steady input signal to one at a higher amplitude. This jump must happen quicker than the system’s response time. This signal is a step function, and it’s essential for calculating rise time.

## The Relationship

Rise time and 3 dB bandwidth are inversely proportional, so you can use them to describe your system’s limit on responding to input signal changes. They have a proportionality constant of about 0.35 when your system’s response time operates as an RC low-pass filter would:

BW ≈ 0.35 / tR

tR ≈ 0.35 / BW

You can use this relationship to determine the parameter in your system you are unsure of. For example, a rise time of 10μs roughly equates to a bandwidth of 35 kHz. Doing so gives you both parameters to reference when looking at your application’s requirements.

## What Does It Mean in Practice?

With a laser diode driver, such as the 4205-DR LaserSource, which has a bandwidth specification of 325 kHz, you can quickly calculate rise time as approximately 1.1μs. Calculating the rise time and determining what your system can support is easy with these drivers, and you can account for all variables in your laser system.

Understanding the relationship between analog bandwidth and rise time isn’t so tricky once you learn how each variable is important but managing the input signal is a different matter. Thankfully, you can use certain devices, like laser diode drivers, to regulate this input signal. At Arroyo Instruments, our drivers can provide a constant current source for all your application needs!