Calculator inputs
The page keeps a single vertical flow, while the input area uses three columns on large screens, two on medium screens, and one on mobile.
Example data table
These examples use the built in default settings and change only the phase shift to show how lock in channels rotate between X and Y.
| Scenario | Signal amplitude (V) | Phase (°) | Base gain (V/V) | X output (V) | Y output (V) | R output (V) |
|---|---|---|---|---|---|---|
| Perfect alignment | 0.012 | 0 | 125 | 1.5 | 0 | 1.5 |
| Moderate phase shift | 0.012 | 30 | 125 | 1.299038 | 0.75 | 1.5 |
| High quadrature mix | 0.012 | 60 | 125 | 0.75 | 1.299038 | 1.5 |
| Pure quadrature case | 0.012 | 90 | 125 | 0 | 1.5 | 1.5 |
Formula used
K = Gpre × Gpost × Km × Rref × Glpf × E
Gx = K × cos(φ)Gy = K × sin(φ)
X = Vin × Gx + Voff,xY = Vin × Gy + Voff,y
R = √[(X - Voff,x)² + (Y - Voff,y)²]θ = atan2(Y - Voff,y, X - Voff,x)
ENBW = C / τFor a common first order model, C is often 0.25. Different filter slopes use different coefficients.
This calculator models a synchronous detector where the reference channel, mixer, filtering, and output chain act as a single conversion path. The in phase channel follows the cosine projection of phase mismatch, while the quadrature channel follows the sine projection.
The vector magnitude removes the phase split between X and Y, so the recovered signal amplitude remains stable when the phase rotates. Sensitivity and headroom help estimate whether the selected range can hold the projected output without overload.
How to use this calculator
- Enter the expected signal amplitude reaching the lock in input.
- Set the reference scale, preamp gain, post detector gain, mixer constant, and low pass gain.
- Add any expansion factor used by the instrument output stage.
- Enter the phase difference between the signal and reference waveforms.
- Set the time constant and ENBW coefficient for your filter model.
- Choose the sensitivity full scale and offsets for both channels.
- Press Calculate Gain to show the result above the form.
- Review the graph, result metrics, and example table. Export the report through the CSV or PDF buttons when needed.
FAQs
1. What does the base conversion gain represent?
It combines the reference scaling, preamplifier gain, detector gain, mixer constant, low pass gain, and output expansion into one overall voltage conversion factor.
2. Why do X and Y outputs change with phase?
A lock in amplifier projects the input onto two orthogonal references. X follows the cosine component, while Y follows the sine component, so phase rotation redistributes signal energy.
3. Why can the recovered amplitude stay constant?
The recovered amplitude uses the vector magnitude of X and Y after offsets are removed. That magnitude is phase independent for an ideal sinusoidal model.
4. What is the mixer constant used for?
It represents how efficiently the multiplier converts the product of the signal and reference into the final DC component after low pass filtering.
5. How should I choose the ENBW coefficient?
Use the coefficient matching your filter order and implementation. A first order estimate often uses 0.25, while steeper filters usually require different values.
6. What does sensitivity usage tell me?
It compares the calculated vector output to the selected full scale range. Higher values mean less headroom and a greater chance of range saturation.
7. Why are offset inputs included?
Real instruments often show residual channel bias from drifts, cable imbalance, or internal electronics. Offsets help the model match measured instrument readings more closely.
8. Can I use this for dual phase tuning?
Yes. Sweep the phase, watch the graph, and adjust settings until X is maximized or Y is minimized, depending on your preferred alignment target.