Engineering Calculators

Bandwidth

BW = 0.35 / t_r × 1000 = 350 / t_r. Enter rise time in ns, read bandwidth in MHz.

BW = 350 ÷ ns

Result: 0 MHz

Rise time

t_r = 0.35 / BW × 1000 = 350 / BW. Enter bandwidth in MHz, read rise time in ns.

t_r = 350 ÷ MHz

Result: 0 ns

System bandwidth

\[ BW_{\text{(DISPLAYED)}} = \frac{1}{\sqrt{ \left( \frac{1}{BW_{\text{(SCOPE)}}} \right)^2 + \left( \frac{1}{BW_{\text{(PROBE)}}} \right)^2 + \left( \frac{1}{BW_{\text{(SOURCE)}}} \right)^2 }} \]

BW_(DISPLAYED) is the displayed bandwidth, BW_(SCOPE) the oscilloscope bandwidth, BW_(PROBE) the probe bandwidth and BW_(SOURCE) the source bandwidth.

BW_(DISPLAYED) =1 / √ 1÷ ² + 1÷ ² + 1÷ ²

Result: 0 MHz

System rise time

t_r = = , where every term is a rise time in ns.

t_r = √ ² + ² + ²

Result: 0 ns

How it works

Bandwidth, rise time and knee frequency are the basis of every dynamic measurement.

Bandwidth (BW) defines the range of frequencies a system can pass; rise time (t_r) describes how fast the signal transitions in the time domain; knee frequency (f_knee) marks the point above which the response rolls off steeply. Relating rise time to bandwidth tells you how much bandwidth the whole measurement chain — probe, cable and instrument — must provide to capture a fast edge faithfully.

Formulas

Rise time and knee frequency are calculated as:

Rise time (t_r):

t_r(ns) =

0.35

BW (GHz)

Knee frequency (f_knee):

f_knee =

0.5

t_r

✓ BW — bandwidth in gigahertz (GHz)

✓ t_r — rise time in nanoseconds (ns)

✓ f_knee — knee frequency in hertz (Hz)

Common-mode rejection ratio (CMRR)

CMRR = 20 log₁₀ |A_d / A_c|, where A_d is the differential gain and A_c the common-mode gain. For A_d = 1000 and A_c = 1 the result is 60 dB.

CMRR = 20log₁₀| ÷ |

Result: 0 dB

How it works

CMRR =

A_d (differential gain)

A_c (common-mode gain)

As A_c approaches zero, CMRR approaches infinity — the ideal differential amplifier. For a differential probe, the higher the CMRR the better.

✓ Higher is better; 80 dB (10 000 : 1) is typical of a good differential probe

✓ CMRR degrades as frequency rises — check the specification at your measurement frequency

Coax shunt: Joule heating

Joule heating: Q = I² × R × t, with I in A, R the shunt resistance in Ω and t the current duration in s.

Q = ² × ×

Result: 0 J

DC power dissipation

P = I² × R, with I in A and R the shunt resistance in Ω.

P = ² ×

Result: 0 W

AC power dissipation

P = I² × R × cos φ, with I in A, R the shunt resistance in Ω and φ the phase angle between voltage and current, entered in degrees.

P = ² × × cos

Result: 0 W

Shunt resistance: unit conversion

1 Ω = 1000 mΩ

Ω = ÷ 1000

Result: 0 Ω

Scope scaling from shunt resistance

Scale factor = 1 / R, with R the shunt resistance in Ω.

Result = 1 ÷

Result: 0

Vertical resolution

R = 1 / 2ⁿ, where n is the ADC resolution in bits (n = 8 for an 8-bit acquisition).

R = 1 / 2

Resolution: 0 %

ADC bits	Vertical resolution
6	1.56%
7	0.78%
8	0.39%
9	0.20%
10	0.098%
11	0.049%
12	0.024%

Voltage ratio to dB

D = 20 log₁₀ (V₂ / V₁), in dB.

D = 20log₁₀| ÷ |

Result: 0 dB

Voltage to dBm (50 Ω)

D = 20 log₁₀ (V / 0.224) for a 50 Ω system, with V the RMS voltage.

D = 20log₁₀| ÷ 0.224 |

Result: 0 dB

Power to dBm

D = 10 log₁₀ (P / 0.001), with P in mW.

D = 10log₁₀| ÷ 0.001 |

Result: 0 dB

Temperature conversion

K = 273.15 + °C

K = 273.15 +

Result: 0 K

Minimum sampling rate

F_s > 2 × system bandwidth (Nyquist).

Fs > 2 * Hz

Result: 0 Hz

Sine-wave amplitude

Enter the peak value V_0-p. Then V_p-p = 2 V_0-p, V_rms = 0.707 V_0-p and V_avg = (2/π) V_0-p.

Input

V_0-p

Output

V_p-p = 2 V_0-p = 0 V

V_rms = 0.707 V_0-p = 0 V

V_avg = (2/π) V_0-p = 0 V

Calculators

Bandwidth

Rise time

System bandwidth

System rise time

How it works

Formulas

Common-mode rejection ratio (CMRR)

How it works

Coax shunt: Joule heating

DC power dissipation

AC power dissipation

Shunt resistance: unit conversion

Scope scaling from shunt resistance

Scope scaling from probe attenuation

Vertical resolution

Voltage ratio to dB

Voltage to dBm (50 Ω)

Power to dBm

Temperature conversion

Minimum sampling rate

Sine-wave amplitude