Step-Up Transformer (SUT) Loading — Full Calculation Guide

Optimise MC cartridge loading with exact math: reflected load, secondary resistor, effective input impedance, and adjusted gain.

Why SUT loading matters

A Step-Up Transformer reflects your MM phono input impedance back to the cartridge. Adding a resistor across the secondary lets you fine-tune that load. Getting it right improves tonal balance, noise performance, headroom and correct system integration.

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Definitions & symbols

\(N\): transformer step-up ratio (e.g. \(1{:}10 \Rightarrow N=10\))
\(Z_{\text{phono}}\): phono input impedance (typically \(47\,\text{k}\Omega\))
\(R_{\text{load}}\): added resistor across the secondary (optional)
\(Z_{\text{sec,tot}}\): total load at the secondary (phono ∥ \(R_{\text{load}}\))
\(Z_{\text{cart}}\): effective input impedance at the primary (what the cartridge “sees”)
\(R_s\): cartridge internal (source) resistance
(Optional) \(R_P\), \(R_S\): primary & secondary DCR (Ω)

1) Secondary load

\[ Z_{\text{sec,tot}} \;=\; Z_{\text{phono}} \,\big\|\, R_{\text{load}} \;=\; \left(\frac{1}{Z_{\text{phono}}}+\frac{1}{R_{\text{load}}}\right)^{-1} \]

2) Primary load (what the cartridge sees)

\[ Z_{\text{cart}} \;=\; \frac{Z_{\text{sec,tot}}}{N^2} \]

No-resistor rule: If \(Z_{\text{target}}\ge Z_{\text{phono}}/N^2\), you cannot raise load with a passive shunt. Leave the secondary unloaded.

3) Solve the added secondary resistor

For a target cartridge load \(Z_{\text{target}}\):

\[ Z_{\text{sec,req}} = N^2\,Z_{\text{target}},\qquad R_{\text{load}} = \left(\frac{1}{Z_{\text{sec,req}}} - \frac{1}{Z_{\text{phono}}}\right)^{-1} \]

Pick the nearest E24 value, then recompute achieved \(Z_{\text{cart}}\) and adjusted gain.

4) Adjusted gain (divider loss)

Cartridge source resistance and the primary load form a divider that trims the ideal ratio \(N\):

\[ \frac{V_{\text{sec}}}{V_{\text{cart}}} = N\cdot \frac{Z_{\text{cart}}}{Z_{\text{cart}}+R_s},\qquad G_{\text{eff,dB}} = 20\log_{10}\!\left(N\cdot \frac{Z_{\text{cart}}}{Z_{\text{cart}}+R_s}\right) \]

Including DCRs: add \(R_P\) in series with the cartridge on the primary; add \(R_S\) in series on the secondary before the parallel network.

5) Worked example

Target 100 Ω with 1:8 into 47 kΩ. Required secondary total \(=6.4\) kΩ; solve gives \(R_{\text{load}}\approx 7.41\) kΩ → use 7.5 kΩ. Achieved \(Z_{\text{cart}}\approx 101\) Ω. With \(R_s\approx 40\) Ω, effective gain ≈ 15.2 dB.

6) Quick decision rules

\(Z_{\text{target}}\ge Z_{\text{phono}}/N^2\) → no resistor.
Otherwise add a shunt across the secondary and re-check \(G_{\text{eff}}\).
If you’re giving up too much gain, consider a different \(N\) or a higher target load.

7) Live calculator

Custom Transformer & E24 Resistor Calculator

Transformer Primary DCR (Ω): Transformer Secondary DCR (Ω): Step-Up Ratio (Ns/Np): Phono Input (kΩ): Desired Cartridge Load (Ω): Cartridge DC Resistance (Ω) (optional): Cartridge Output (mV) (optional):

Tip: Press Enter to calculate.

E24 Resistor Recommendation
Theoretical Resistor:	N/A
Nearest E24 Resistor:	N/A
Effective Input Impedance:	N/A
Voltage Gain:	N/A
Output Voltage:	N/A

How to use

Enter transformer DCRs (Ω) and step-up ratio.
Enter phono input in kΩ (e.g. 47 for 47 kΩ).
Enter your desired cartridge load (Ω). Optionally add cartridge DC resistance and output in mV.
Click Calculate or press Enter.

“Effective Input Impedance” = Primary DCR + reflected (Secondary DCR + parallel of phono input and E24 shunt)/n². Gain includes transformer ratio, DCR losses, and loading.

Step Up Transformers Explained