The Full Power Bandwidth (FPBW) of an op-amp defines the maximum frequency at which the amplifier can produce its maximum output voltage swing without experiencing slew rate limiting. This means that at frequencies above the FPBW, the output signal will become distorted because the amplifier's rate of change cannot keep up with the required voltage change.
The exact formula for calculating the full power bandwidth ($FPBW$) is derived from the amplifier's slew rate ($SR$) and its maximum peak output voltage ($V_p$). It is given by:
$$FPBW = \frac{SR}{2 \cdot \pi \cdot V_p}$$
Key Components of the Full Power Bandwidth Formula
| Component | Symbol | Unit | Description |
|---|---|---|---|
| Full Power Bandwidth | $FPBW$ | Hertz (Hz) | The highest frequency at which an operational amplifier can output its maximum specified voltage swing without distortion caused by slew rate limitations. |
| Slew Rate | $SR$ | V/µs or V/s | The maximum rate of change of the output voltage of an op-amp. It indicates how quickly the output can respond to large, rapid changes in the input signal. For accurate calculations, it should be in V/s. Learn more about slew rate. |
| Peak Output Voltage | $V_p$ | Volts (V) | The maximum undistorted peak voltage that the op-amp can deliver at its output. This value is often denoted as $V_0$ in many engineering contexts and is typically specified in the op-amp's datasheet. |
| Two Pi | $2 \cdot \pi$ | Dimensionless | A mathematical constant (approximately $6.283185$) fundamental to sine wave analysis, converting between angular frequency (radians per second) and linear frequency (Hertz). |
Calculating Full Power Bandwidth: Practical Example
To calculate the $FPBW$ for a given op-amp, follow these steps:
- Identify the Slew Rate ($SR$): Obtain this value from the op-amp's datasheet. Ensure consistent units; if it's in V/µs, convert it to V/s by multiplying by $10^6$.
- Determine the Peak Output Voltage ($V_p$): This is the maximum specified undistorted output voltage swing of the op-amp, also found in the datasheet.
- Apply the Formula: Substitute the collected values into the $FPBW$ equation.
Example Calculation:
Consider an op-amp with the following specifications:
- Slew Rate ($SR$): $10 \, V/\mu s$
- Maximum Peak Output Voltage ($V_p$): $10 \, V$
First, convert the slew rate to V/s:
$SR = 10 \, V/\mu s = 10 \times 10^6 \, V/s$
Now, apply the FPBW formula:
$FPBW = \frac{10 \times 10^6 \, V/s}{2 \cdot \pi \cdot 10 \, V}$
$FPBW = \frac{10,000,000}{62.83185} \, Hz$
$FPBW \approx 159,155 \, Hz \approx 159.16 \, kHz$
This calculation indicates that the op-amp can amplify a $10 \, V$ peak sine wave up to approximately $159.16 \, kHz$ without the output signal being distorted by slew rate limiting. Above this frequency, the output waveform would become more triangular as the op-amp struggles to maintain the required rate of change.
Factors Influencing Full Power Bandwidth
The FPBW is fundamentally limited by the slew rate, which itself can be influenced by several design and operational factors:
- Power-Supply Voltage: The available power-supply voltage directly impacts the maximum achievable peak output voltage ($V_p$), thereby affecting the FPBW.
- Load Conditions: The electrical load connected to the amplifier's output can influence its ability to deliver current, which may, in turn, affect the actual undistorted peak output voltage and, consequently, the FPBW.
- Internal Circuitry: The internal architecture and compensation networks of an op-amp are critical in determining its inherent slew rate.
While the core formula universally describes the full power bandwidth, in more detailed or application-specific circuit analyses, additional parameters might be considered. For example, in complex system models or impedance matching considerations, terms such as $Z_1$ and $Z_2$ could be introduced to represent specific circuit impedances or transfer function elements that influence the overall frequency response or power delivery characteristics. These terms provide a more granular view of how different parts of a circuit interact to define its performance boundaries.
