PXIe-4190 Specifications

Total Measurement Time per setpoint = LCR Source Delay + Total LCR Measurement Time

Calculating LCR Source Delay Time

• LCR Source Delay Mode = Automatic
  • In Automatic mode, the source delay is 20 cycles of the AC stimulus frequency with a minimum source delay of 1 ms.
  • $\mathrm{LCR\; Source\; Delay}=\mathrm{Maximum}(20\times \frac{1}{f},\mathrm{1\; ms})$

• LCR Source Delay Mode = Manual
  • LCR Source Delay time is as specified for the Source Delay property.
  Note Using a source delay smaller than the default value may not allow the output to sufficiently settle, resulting in measurement inaccuracy.
• Setpoint changes that result in a range change add an additional 600 μs of source delay in either mode.

Calculating Total LCR Measurement Time

• $\mathrm{Total\; LCR\; Measurement\; Time}=N\times (\mathrm{CoercedMeasurementTime}+\mathrm{10\; \mu s})$

  • N—Measurement count

  • CoercedMeasurementTime—
    • The measurement time coerces to a full sinewave cycle boundary regardless of mode.
      $\lceil x\rceil =\mathrm{Ceiling\; function}$
    • $\mathrm{CoercedMeasurementTime}=\frac{\lceil \mathrm{LCR\; Measurement\; Time}\times f\rceil }{f}$

      Where LCR Measurement Time = Short (1 ms)/Medium (10 ms))/Long (100 ms)/Custom

      Note LCR Custom Measurement Time = 0 is a special case that gives 1 cycle for any frequency.

Above 500 kHz with DC Bias enabled, add the additional error term to the stated magnitude accuracy specification:

Above 500 kHz with DC Bias enabled, add the additional error term to the stated phase accuracy specification:

LCR DC Bias Settling Time for Large Capacitors

Set DC Bias ALC to Off when measuring capacitors over 1 uF to minimize settling time.

Table 18. DC Bias Settling Time Required in Addition to LCR Source Delay for Large Capacitors

Bias	Settling Time
AC Stimulus Voltage / Impedance Range ≤ 7.07 mA	Add 3 ms per µF of DUT capacitance
AC Stimulus Voltage / Impedance Range > 7.07 mA	Add 600 µs per µF of DUT capacitance
Note: When applying a bias voltage to capacitors over 1 mF, the bias voltage steps should be no larger than 40 V x 1 mF/C to avoid tripping overcurrent protection. Note: For AC Stimulus Voltage / Impedance Range ≤7.07mA, limit DC bias steps to ≤5 V each, up to 40 V total.

The impedance range can be calculated and programmed in several ways. The following methods allow you to set the impedance range directly.

Calculating Impedance Range Manually

Use the following formulas to determine the expected impedance based on the load.

The impedance of an ideal capacitor is

Z_C—Capacitor impedance (Ω)

f—AC stimulus frequency (Hz)

C—Nominal capacitance value (F)

The impedance of an ideal inductor is

Z_L—Inductor impedance (Ω)

f—AC stimulus frequency (Hz)

L—Nominal inductance value (H)

Setting LCR Impedance Range Source Programmatically

By setting LCR Impedance Range Source to LCR Load Configuration, the range can be determined automatically based on the AC stimulus frequency, and the load settings LCR Load Resistance, LCR Load Inductance, and LCR Load Capacitance.

Accuracy for additional impedance parameters can be derived from the absolute impedance magnitude and phase specifications. For some calculations, the actual DUT impedance must also be known—in these cases, the measured value can be used as an approximation with typically negligible impact on the result.

∆x_Spec—Specified accuracy for a parameter x (for example, Δ|Z|_Spec is the magnitude accuracy specification)

x_DUT—The actual value of parameter x for a DUT

|Z|—Impedance magnitude. Δ|Z|_Spec corresponds to the numbers listed in the magnitude accuracy tables (in percent).

θ—Impedance phase angle. Δθ_Spec corresponds to the numbers listed in the phase accuracy tables (in degrees).

δ—Phase angle between the impedance vector and the reactive axis.

$\Delta {\delta }_{\mathrm{Spec}}=\Delta {\theta }_{\mathrm{Spec}}\left(°\right)$

D—Dissipation factor.

$D=\tan \left(\delta \right)=\frac{R}{\left|X\right|}$

$\Delta D_{\mathrm{Spec}}=\pm \tan \left(\Delta {\theta }_{\mathrm{Spec}}\right)$

(when D_DUT < 0.1).

Q—Quality factor,

$Q=\frac{1}{D}$

To determine the specified range of possible Q values, calculate

$\frac{1}{D_{\text{DUT}}\pm \Delta D_{\text{Spec}}}$

(when D_DUT < 0.1).

C—Capacitance, series (C_S) or parallel (C_P) equivalent model.

When D_DUT is sufficiently small (<0.1), ΔC_Spec ≅ Δ|Z|_Spec (%).

For a general solution, determine accuracy using the AC stimulus frequency and reactance specification:

$\Delta C_{\mathrm{Spec}}=\pm \frac{1}{2\pi f\times \Delta X_{\mathrm{Spec}}}\left(F\right)$

L—Inductance, series (L_S) or parallel (L_P) equivalent model.

When D_DUT is sufficiently small (<0.1), ΔL_Spec ≅ Δ|Z|_Spec (%).

For a general solution, determine accuracy using the AC stimulus frequency and reactance specification:

R—Resistance, the real component of complex impedance.

For typical non-reactive resistance measurements (D_DUT > 10), ΔR_Spec ≅ Δ|Z|_Spec (%).

To determine accuracy for an arbitrary impedance, first find the maximum and minimum values, R_Max and R_Min, from four calculations:

$({\left|Z\right|}_{\mathrm{DUT}}\pm \Delta {\left|Z\right|}_{\mathrm{Spec}})\times \cos ({\theta }_{\mathrm{DUT}}\pm \Delta {\theta }_{\mathrm{Spec}}),$

then

$\Delta R_{\mathrm{Spec}}=\pm \frac{R_{\mathrm{Max}}-R_{\mathrm{Min}}}{2}\left(\Omega \right)$

X—Reactance, the imaginary component of complex impedance.

For typical L/C measurements (D_DUT < 0.1), ΔX_Spec ≅ Δ|Z|_Spec (%).

To determine accuracy for an arbitrary impedance, first find the maximum and minimum values, R_Max and R_Min, from four calculations:

$({\left|Z\right|}_{\mathrm{DUT}}\pm \Delta {\left|Z\right|}_{\mathrm{Spec}})\times \sin ({\theta }_{\mathrm{DUT}}\pm \Delta {\theta }_{\mathrm{Spec}}),$

then

$\Delta X_{\mathrm{Spec}}=\pm \frac{X_{\mathrm{Max}}-X_{\mathrm{Min}}}{2}\left(\Omega \right)$

The following figure shows the relationship between these parameters when an example vector Z is plotted on the complex impedance plane.

Example 1: Calculating Specifications for Capacitance Measurement

For a capacitor measurement under the stated conditions, complete the following steps to determine and interpret the absolute measurement accuracy.

1. Calculate ideal capacitor impedance as
   $Z_{\mathrm{DUT}}=\frac{1}{2\pi \mathrm{fC}}=\frac{1}{2\times \pi \times \mathrm{1\; MHz}\times \mathrm{10\; pF}}=15.915\text{k}\Omega$
2. Based on the 1 V RMS AC stimulus, the applicable magnitude and phase specs are found in Table 10 and Table 14, respectively.
   • From the calculated impedance, Z_DUT, the relevant impedance range is 10 kΩ – 100 kΩ.
   • 1 MHz is on the boundary between the 500 kHz to 1 MHz and 1 MHz to 2 MHz frequency ranges, so choose the smaller of the adjacent values.
   • The resulting specifications are 0.3% magnitude accuracy and 0.13° phase accuracy.
3. Base specifications apply to long measurement time. For short measurement time, apply the derating factor:
   $\mathrm{Max}\left(\text{1.5, log}\left(\frac{\left|Z\right|}{V_{\mathrm{stim}}\times 5\times {10}^4}\right)\right)=\mathrm{Max}(\mathrm{1.5,\; log}\left(\frac{\text{15.915 k}\Omega }{\text{1 V}\times 5\times {10}^4}\right))=\mathrm{Max}\left(\mathrm{1.5,\; 0.5}\right)=1.5$
   • The derated magnitude specification is then 1.5 * 0.3% = 0.45%
   • The derated phase specification is then 1.5 * 0.13° = 0.195°
4. Because DC bias is enabled and f >500 kHz, the additional error terms from LCR Accuracy Derating with DC Bias apply:
   • The additional magnitude error is calculated as
     $\frac{f\times V_{\text{DC}}\times \text{0.0015\%}}{\text{500 kHz}}=\frac{\text{1 MHz}\times \text{10 V}\times \text{0.0015\%}}{\text{500 kHz}}=\text{0.03\%}$
   • The additional phase error is calculated as
     $\frac{f\times V_{\text{DC}}\times \text{0.005°}}{\text{500 kHz}}=\frac{\text{1 MHz}\times \text{10 V}\times \text{0.0005°}}{\text{500 kHz}}=\text{0.01°}$
5. From the previous steps, the final accuracy specifications under these measurement conditions:
   • Magnitude accuracy, ΔZ_Spec = 0.45% + 0.03% = 0.48%
   • Phase accuracy, Δθ_Spec = 0.195° + 0.01° = 0.205°

These specifications can then be used to derive accuracies for other parameters.

• Dissipation factor accuracy, ΔD_Spec = ±tan(Δθ_Spec) = ±0.0036
  • Specified range is D_DUT ± ΔD_Spec = 0.0013 to 0.0087
• Quality factor specified range is
  $\frac{1}{D_{\text{DUT}}\pm \Delta D_{\text{Spec}}}=\text{115 to 769}$
• Impedance phase has an accuracy of Δθ_Spec = 0.205° and can be expressed as
  • Loss angle, δ_DUT = arctan(D_DUT) = arctan(0.005) = 0.286° ± 0.205°
  • Impedance phase angle, θ_DUT = δ – 90° = 0.286° - 90° = -89.714° ± 0.205°
• Resistance accuracy, ΔR_Spec, can be calculated by
  • Finding the maximum and minimum values, R_Max and R_Min, from four calculations:
    $(Z_{\text{DUT}}\pm \Delta Z_{\text{Spec}})\times \text{cos}({\theta }_{\text{DUT}}\pm \Delta {\theta }_{\text{Spec}})$
    $=(\text{15.915 k}\Omega \pm \text{0.48\%})\times \text{cos}(\text{-89.714°}\pm \text{0.205°})$
    $=[\text{15.991 k}\Omega \times \text{cos}\left(\text{-89.919°}\right),\text{15.991 k}\Omega \times \text{cos}\left(\text{-89.509°}\right),\text{15.839 k}\Omega \times \text{cos}\left(\text{-89.919°}\right),\text{15.839 k}\Omega \times \text{cos}\left(\text{-89.509°}\right)]$
    $=[\text{22.6}\Omega ,\text{137}\Omega ,\text{22.4}\Omega ,\text{135.7}\Omega ]$
  • Selecting the maximum and minimum values, R_Max = 137 Ω, R_Min = 22.4 Ω
  • $\Delta R_{\text{Spec}}=\frac{R_{\text{Max}}-R_{\text{Min}}}{2}=\frac{\text{137}\Omega -\text{22.4}\Omega }{2}=\pm \text{57.3}\Omega$
• Reactance accuracy, ΔX_Spec, can be calculated by
  • Since D_DUT is small, ΔX_Spec ≅ Δ|Z|_Spec
  • Using this simplified approximation, ΔX_Spec = 0.48% * 15.915 kΩ = ± 76.4 Ω
  • For example, to compare the explicitly calculated specification, first find the maximum and minimum values, X_Max and X_Min, from the four calculations:
    $(Z_{\text{DUT}}\pm \Delta Z_{\text{Spec}})\times \text{sin}({\theta }_{\text{DUT}}\pm \Delta {\theta }_{\text{Spec}})$
    $=(\text{15.915 k}\Omega \pm \text{0.48\%})\times \text{sin}(\text{-89.714°}\pm \text{0.205°})$
    $=[\text{15.991 k}\Omega \times \text{sin}\left(\text{-89.919°}\right),\text{15.991 k}\Omega \times \text{sin}\left(\text{-89.509°}\right),\text{15.839 k}\Omega \times \text{sin}\left(\text{-89.919°}\right),\text{15.839 k}\Omega \times \text{sin}\left(\text{-89.509°}\right)]$
    $=[\text{-15.991 k}\Omega ,\text{-15.990 k}\Omega ,\text{-15.839 k}\Omega ,\text{-15.838 k}\Omega ]$
  • Selecting the maximum and minimum values, X_Max = -15.838 kΩ, X_Min = -15.991 kΩ
  • $\Delta X_{\text{Spec}}=\frac{X_{\text{Max}}-X_{\text{Min}}}{2}=\frac{\text{-15.838 k}\Omega -\text{-15.991 k}\Omega }{2}=\pm \text{76.5}\Omega$