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MSO5000 Liveview — Power Analysis Signal Chain and Math

Goal: Transparently document how the app acquires waveforms from a Rigol MSO5000, converts them to physical units, scales current from probe settings, and computes P, S, Q, PF, phase, and energy. This is a read-only spec of the current code path (v0.9.8h-testing).

Version: 2025-08-12 11:00 UTC

1) Measurement topology (operator responsibilities)

  • Voltage channel (V): select a scope channel (e.g., CH1) that measures the line/load voltage. Keep the scope channel UNIT = VOLT. Enable 20 MHz BW limit on the scope if high-frequency noise hurts RMS/PF.
  • Current channel (I): two supported modes:
  • Shunt mode: measure the shunt’s voltage drop with a differential probe. In the GUI set Probe Type = Shunt and Value = R_shunt in Ω (e.g., 0.01 for 10 mΩ). The app converts this to a current scale A/V by 1/R_shunt.
  • Clamp mode: measure the probe’s volts-per-amp output. In the GUI set Probe Type = Clamp and Value = mV/A (e.g., a 10 mV/A clamp → enter 10). The app converts to A/V via 1 / (mV/A ÷ 1000).
  • Scope unit guardrail: if the current channel is set to UNIT = AMP on the scope, the app forces scale = 1 to avoid double-scaling. Keep the current channel in VOLT unless the scope itself is doing the current conversion.
  • Probe factors: if your differential probe is set to 5×, set the channel PROB=5× so the scope reports the true voltage. With shunts this cancels to unity overall (you still enter the shunt value in ohms).
  • Kelvin at the shunt: sense directly across the shunt pads, short twisted leads, minimal loop area. Prefer low-side shunt to avoid common-mode issues.

2) SCPI acquisition and conversion to volts

The app fetches waveforms over SCPI in NORM or RAW-25M modes using :WAV:* commands. For each selected channel:

  1. Configure:
  2. :WAV:FORM BYTE
  3. :WAV:MODE NORM (or RAW for 25M)
  4. :WAV:POIN:MODE RAW and set :WAV:POIN (NORM) or 25M points (RAW)
  5. Select source and read preamble + data:
  6. :WAV:SOUR CHANn (or MATHn)
  7. :WAV:PRE? → parse XINC, XORIG, YINC, YORIG, YREF
  8. :WAV:DATA? → raw byte array
  9. Convert raw to physical volts:
    \[ v(t) = (raw - YREF)\cdot YINC + YORIG \]

If 25M mode is used, the app stops the scope, fetches, then RUN resumes. If the two channels’ lengths mismatch, the longer one is resampled so V and I align sample-by-sample.

3) Current scaling (V → A)

After converting the current channel to volts, the app multiplies by a current scale (A/V):

  • Shunt: scale = 1 / R_shunt (R in Ω).
  • Clamp: scale = 1 / (mV_per_A / 1000) (Value field is mV/A).
  • Scope in AMP: if the current channel unit is AMP, the app sets scale = 1 (no extra scaling) to avoid double conversion.

Then:
\[ i(t) = v_{\text{current}}(t) \times \text{scale} \]

A user Correction Factor multiplies the base scale (default 1.0) and is applied uniformly.

4) Optional conditioning

  • DC removal: by default the compute path removes mean values of V and I prior to power/phase calculations:
    \[ v \leftarrow v - \overline{v}, \quad i \leftarrow i - \overline{i} \]
    This protects against small offsets skewing PF/phase on AC. (Configurable at call site.)
  • Bandwidth: any BW limiting is performed on the scope (e.g., 20 MHz). The app uses whatever the scope sends.

5) Core calculations

Given aligned arrays \( v(t), i(t) \) with sampling interval \( \Delta t = XINC \):

5.1 RMS

\[ V_\mathrm{rms} = \sqrt{\mathrm{mean}(v^2)}, \qquad I_\mathrm{rms} = \sqrt{\mathrm{mean}(i^2)}. \]

5.2 Instantaneous power and real power

\[ p(t) = v(t)\,i(t), \qquad P = \mathrm{mean}(p(t)). \]

5.3 Apparent power

\[ S = V_\mathrm{rms}\, I_\mathrm{rms}. \]

5.4 Phase and reactive power

The app estimates the fundamental phase of V and I from the FFT bin 1: \[ \phi_v = \angle \mathrm{FFT}(v)[1], \quad \phi_i = \angle \mathrm{FFT}(i)[1], \quad \Delta \phi = \phi_v - \phi_i. \] Reactive power is computed as: \[ Q = S \cdot \sin(\Delta \phi). \]

5.5 Power factor

\[ \mathrm{PF} = \frac{P}{S} \quad (\text{signed with }\mathrm{sign}(P)). \]

Note: Using the fundamental for phase is robust for periodic signals. For non-sinusoidal waveforms, \(P\) still comes from \( \mathrm{mean}(v\,i) \), while \(Q\) is derived from the fundamental phase. This is stated here for traceability.

6) Numeric integration for energy

During a session the app reports energy by multiplying the running averages by elapsed time \(T\) (hours): \[ E_\mathrm{Wh} = \overline{P}\,T,\;\; E_\mathrm{VAh} = \overline{S}\,T,\;\; E_\mathrm{VARh} = \overline{Q}\,T. \] These are logged periodically to CSV together with Vrms/Irms and PF.

7) Safety/guardrails in the compute path

  • Unit check: if the current channel UNIT? = AMP, force scale = 1.0 to avoid double-scaling and log that choice.
  • Probe reporting: the app logs the current channel’s :PROB? for visibility (no extra math).
  • Length mismatch: if V and I sample counts differ, the longer series is interpolated to align lengths before FFT and power math.

8) Logging and reproducibility

  • On-screen “Analysis Output” shows instantaneous and running averages for P, S, Q, PF, Vrms, Irms, impedance \(Z = V_\mathrm{rms}/I_\mathrm{rms}\), PF angle \( \theta = \arccos(\mathrm{PF}) \), and elapsed iterations/time.
  • CSV logging (Power tab): oszi_csv/power_log_YYYYMMDD_HHMMSS.csv with columns:
    Timestamp, P (W), S (VA), Q (VAR), PF, PF Angle (°), Vrms (V), Irms (A), Real Energy (Wh), Apparent Energy (VAh), Reactive Energy (VARh).
  • Long-time logger: when logging channels, if a channel’s UNIT is AMP the logger writes values as-is; otherwise it applies the provided current scale. Results per channel include Vpp/Vavg/Vrms (optionally) multiplied by the scale.
  • Channel snapshot: the SCPI loop records scale, offset, coupling, probe for active CH1–CH4 and MATH types for MATH1–3; the “Channel Data” tab renders this, aiding traceability of scope-side settings.

9) Operator checklist (to maximize accuracy)

  1. Topology: Prefer low-side shunt; Kelvin connections on shunt pads; twisted pair, small loop.
  2. Scope config: VOLT units on both channels; PROB matches hardware (e.g., 5×/5×); enable 20 MHz BW limit when appropriate.
  3. GUI entries:
  4. Shunt: enter R (Ω) exactly (e.g., 0.01 for 10 mΩ).
  5. Clamp: enter mV/A exactly (e.g., 10 for 10 mV/A).
  6. Corr = 1.0 unless you have a traceable calibration factor.
  7. Sanity check: compare CH(current) Vrms on scope vs. expected \( I \cdot R \) (shunt) or \( V/A \) (clamp). For shunt=10 mΩ at 1.7–1.8 A you should see ~17–18 mV on the current channel.
  8. Phase reference: keep the frequency reference stable; deskew at the scope if needed.

10) Definitions summary

  • \( p(t) = v(t)\,i(t) \) — instantaneous power
  • \( P = \mathrm{mean}(p) \) — real/active power (W)
  • \( S = V_\mathrm{rms} I_\mathrm{rms} \) — apparent power (VA)
  • \( Q = S \sin\Delta\phi \) — reactive power (var)
  • \( \mathrm{PF} = P/S \) (signed by \(P\))
  • \( Z = V_\mathrm{rms}/I_\mathrm{rms} \) — magnitude only; angle from \( \theta = \arctan2(Q, P) \)

11) Notes on limitations

  • The phase angle \( \Delta\phi \) comes from the fundamental (FFT bin 1). With heavily non-sinusoidal waveforms, \(P\) remains exact from \(v\cdot i\), while \(Q\) and PF reflect the fundamental component’s phase.
  • Energy numbers are average-based (not trapezoidal time integration of \(p(t)\)). Over long windows this matches within the averaging tolerance.