Measurements & Instrumentation Formula Book

10.1

Energy Meter: Speed & Temperature Compensation

6. Temperature Compensation — MUTEMP

T↑ → disc R↑ → eddy current↓ | MUTEMP: μ↓ → B↓ → braking↓ → net speed constant

7. Speed Adjustment

T_b \propto N_\phi^2\,d \quad\Rightarrow\quad N \propto \frac{1}{\phi^2\,d}

Position of brake magnet from spindle controls disc speed

Creeping Error

\%\text{Creep} = \frac{\text{Rev due to creeping/hr}}{\text{Rev due to load/hr}} \times 100

Causes: over-friction compensation, over-voltage, excessive lubrication, vibration, stray fields

Elimination: two holes drilled on opposite sides of disc

MUTEMP Temperature Compensation

Temp (°C) 25

Without MUTEMP: Speed ↑ With MUTEMP: Speed OK ✓

Brake Magnet Position

Position 50%

Medium braking → Medium speed

Creeping Demonstration

⚙️ Creeping Error Calculator

Creep rev/hr: Load rev/hr:

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10.2

Cathode Ray Oscilloscope (CRO): Overview

Electronic instrument for waveform display | Voltage sensitive | Principle: Thermionic emission

y-t mode → RMS, Peak, Average, Time period

x-y mode (Lissajous) → Phase, Frequency

CRT Parts: 1. Electron gun (Cathode) | 2. Pre-accelerating & Accelerating anode | 3. Horizontal deflecting plates | 4. Vertical deflecting plates

Sine wave | y-t mode

10.3

CRO Deflection: Electrostatic vs Magnetic

Electrostatic Deflection:

\boxed{D = \frac{L\,\ell_d\,V_d}{2\,d\,E_a}} \quad S = \frac{L\,\ell_d}{2\,d\,E_a}\;\text{m/V} \quad G = \frac{1}{S}\;\text{V/m}

Magnetic Deflection:

S_m \propto \frac{1}{\sqrt{E_a}} \quad D \propto \frac{I_d}{\sqrt{E_a}}

Electrostatic: S ∝ 1/E_a | Magnetic: S_m ∝ 1/√E_a → Magnetic better at high E_a

BW \times t_r = 0.35

Parameter	Electrostatic	Magnetic
Deflection D	Lℓ_dV_d/(2dE_a)	∝ I_d/√E_a
Sensitivity S	Lℓ_d/(2dE_a) m/V	∝ 1/√E_a
Best for	High freq CRO	TV, radar
Freq range	DC to GHz	DC to few MHz

V_d (V) 80

D = — mm S = — mm/V

📐 Electrostatic Deflection Calculator

L (m): ℓ_d (m): d (m): E_a (V): V_d (V):

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⏱️ Bandwidth–Rise Time

BW (MHz):

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10.4

Lissajous Patterns: Frequency & Phase

\boxed{f_x = f_y \cdot \frac{N_h}{N_v}}

\boxed{\sin\phi = \frac{Y_0}{Y_{max}} = \frac{X_0}{X_{max}}}

φ=0°: line (I,III) | 0°<φ<90°: ellipse (I,III) | φ=90°: circle | φ=180°: line (II,IV)

f_x/f_y φ 90°

N_h = 1 N_v = 1 Circle

🌀 Lissajous Frequency Calculator

f_y (Hz): N_h: N_v:

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📐 Phase from Ellipse

Y₀: Y_max:

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10.5

CRO Measurements: y-t Mode

V_{pp} = n_{div} \times V/div \quad V_p = V_{pp}/2 \quad V_{rms} = V_p/\sqrt{2}

T = n_{div} \times T/div \quad f = 1/T

t_r = \text{10\% to 90\%} \quad BW = 0.35/t_r

\phi = \frac{\Delta t}{T}\times 360°

1× probe: no attenuation, R_in=1MΩ | 10× probe: V/10, R_in=10MΩ (less loading)

V/div T/div

Phase Δt/T 25%

V_p = — V_rms = — f = — φ = —

📺 y-t Measurement Calculator

n_div (V): V/div: n_div (T): T/div (ms):

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📐 Phase Difference (Dual Trace)

Δt (ms): T (ms):

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10.6

CRO: Complete Reference

S = \frac{L\ell_d}{2dE_a},\; G = \frac{2dE_a}{L\ell_d},\; D = S \cdot V_d

BW \times t_r = 0.35

f_x = f_y\cdot\frac{N_h}{N_v},\; \phi = \sin^{-1}\!\left(\frac{Y_0}{Y_{max}}\right)

V_{rms} = \frac{n_{div}\times V/div}{2\sqrt{2}},\; f = \frac{1}{n_{div}\times T/div}

Measurement	Method + Formula
V_peak	y-t: n_div × V/div
V_rms	V_p/√2
Frequency	y-t: 1/(n_div × T/div)
Phase	x-y: sin⁻¹(Y₀/Y_max)
Freq ratio	Lissajous: N_h/N_v
Rise time	10% to 90% step
Bandwidth	0.35/t_r

Amp Freq

V_p V_rms T f

📊 CRO Master Calculator

n_div(V): V/div: n_div(T): T/div(ms):

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Module 10 — CRO & Electronic Measurements