Transformer Impedance Ratio Calculator
Calculate ideal magnetic transformer impedance reflection with the square-law relationship. TRF-002 keeps the same primary-to-secondary turns convention as TRF-001: a = Np/Ns.
Engineering tool
Transformer Impedance Ratio Calculator
Calculate ideal transformer impedance reflection using the square-law relationship Zp/Zs = (Np/Ns)².
Used with secondary turns to calculate a = Np/Ns.
The ratio direction stays primary divided by secondary.
Impedance magnitude connected to or referred on the secondary side.
Result console
- Primary-Referred Impedance
- 800Ω
- Turns Ratio a = Np/Ns
- 10
- Impedance Ratio a²
- 100
- Normalized Turns Ratio
- 10 : 1
- Reflection Direction
- Secondary to Primary
- Secondary Impedance
- 8Ω
Ideal impedance magnitude reflection only. This tool does not calculate magnetizing impedance, leakage inductance, VA loading, efficiency, voltage regulation, flux density, flyback design, or RF quarter-wave transmission-line transformers.
Formula reference
Transformer impedance ratio formulas
The impedance ratio is square-law. A 10:1 turns ratio produces a 100:1 impedance ratio.
a = Np/NsZp/Zs = a²Zp = Zs × a²Zs = Zp/a²a = sqrt(Zp/Zs)Variable definitions
- a
- primary-to-secondary turns ratio
- Zp
- impedance referred to the primary side
- Zs
- impedance referred to the secondary side
- Np
- primary turns
- Ns
- secondary turns
TRF-002 Formula Audit
| Turns Ratio Convention | a = Np/Ns, reused from TRF-001. |
|---|---|
| Impedance Ratio Convention | Zp/Zs = a². |
| Primary Reflection Formula | Zp = Zs × a². |
| Secondary Reflection Formula | Zs = Zp/a². |
| Required Turns Ratio Formula | a = sqrt(Zp/Zs). |
| Square-Law Boundary | A 10:1 turns ratio gives 100:1 impedance ratio, not 10:1. |
| Complex Impedance Scope | Ideal formula also applies to complex impedance, but V1 UI accepts positive impedance magnitude. |
| Frequency Boundary | No frequency input; real frequency response requires parasitic and magnetizing models. |
| TRF-011 Boundary | TRF-011 remains planned for broader load/current context; TRF-002 is the pure impedance-ratio tool. |
| RF Boundary | No quarter-wave line length, Smith chart, balun, or transmission-line matching model. |
Worked Examples
| Case | Calculation | Result |
|---|---|---|
| Impedance ratio | Np=1000, Ns=100 | a=10, a²=100 |
| Primary reflection | Zs=8Ω, a=10 | Zp=800Ω |
| Secondary reflection | Zp=800Ω, a=10 | Zs=8Ω |
| Step-up turns case | Np=100, Ns=1000, Zs=800Ω | a=0.1, Zp=8Ω |
| Required turns ratio | Zp=600Ω, Zs=8Ω | a=sqrt(75)=8.660254 |
| 1:1 impedance | Zp=50Ω, Zs=50Ω | a=1, impedance ratio=1 |
| Unit scaling | Zs=8kΩ, a=2 | Zp=32kΩ |
| Secondary from MΩ | Zp=1MΩ, a=10 | Zs=10kΩ |
| Square-law scale | Zs=8Ω, a=2 then a=4 | 32Ω then 128Ω |
| Round trip | Zs=4Ω, a=5 | Zp=100Ω, reverse returns 4Ω |
Engineering Notes
- TRF-002 inherits the Transformers convention a = Np/Ns from TRF-001.
- Impedance reflection uses the square of turns ratio, not the linear turns ratio.
- Primary-referred impedance is the secondary impedance viewed through the transformer from the primary side.
- Secondary-referred impedance is the primary impedance viewed through the transformer from the secondary side.
- A 10:1 transformer reflects an 8 ohm secondary load as 800 ohms on the primary side.
- The calculator accepts impedance magnitude, so pure resistance examples are valid.
- For complex impedance, the ideal relation Zp = a²Zs preserves phase angle because a² is real and positive.
- The ideal reflection formula does not require frequency.
- Real transformer input impedance varies with frequency because of magnetizing inductance, leakage inductance, core loss, winding resistance, and parasitic capacitance.
- Reflected impedance is not the same thing as winding resistance.
- This tool does not calculate magnetizing impedance or no-load current.
- This tool does not calculate transformer VA rating, loading percentage, efficiency, regulation, or flux density.
- Audio transformer examples are useful first-pass checks, but bandwidth, saturation, and power rating still matter.
- RF quarter-wave transformer calculators are transmission-line tools, not this magnetic transformer impedance-ratio model.
Common Mistakes
- Using linear turns ratio for impedance instead of squaring it.
- Squaring the impedance ratio a second time.
- Reversing Np/Ns while keeping the same formula.
- Reversing primary and secondary impedance labels.
- Using Ns/Np without changing the reflection direction.
- Calling every impedance value resistance.
- Assuming reflected impedance equals winding resistance.
- Ignoring real transformer parasitics.
- Assuming this formula predicts input impedance at every frequency.
- Mixing kΩ and Ω values.
- Rounding turns ratio too early.
- Confusing magnetic transformer impedance reflection with RF quarter-wave line matching.
Support reference
FAQ
What is transformer impedance ratio?
Transformer impedance ratio is the ratio between primary-referred impedance and secondary impedance. With a = Np/Ns, the ideal relation is Zp/Zs = a².
How do I calculate transformer impedance ratio?
Calculate the primary-to-secondary turns ratio a = Np/Ns, then square it. A 10:1 turns ratio gives a 100:1 impedance ratio.
Why is impedance ratio the square of turns ratio?
Voltage scales by a while current scales inversely in the primary-to-secondary direction. Since impedance is voltage divided by current, the combined effect is a².
What does primary-referred impedance mean?
Primary-referred impedance is the impedance that a secondary load appears to have when viewed from the primary winding in the ideal transformer model.
How do I reflect a secondary load to the primary?
Use Zp = Zs × a², where a = Np/Ns.
How do I reflect a primary impedance to the secondary?
Use Zs = Zp/a².
How do I calculate required turns ratio from two impedances?
Use a = sqrt(Zp/Zs). For 600 ohms primary and 8 ohms secondary, a is sqrt(75), about 8.6603.
What is the formula for transformer impedance matching?
For an ideal magnetic transformer, Zp/Zs = (Np/Ns)². This calculator handles that magnetic transformer relationship, not transmission-line matching.
Does a 10:1 turns ratio give a 10:1 impedance ratio?
No. A 10:1 turns ratio gives a 100:1 impedance ratio.
What impedance ratio does a 10:1 transformer have?
A 10:1 primary-to-secondary turns ratio has a 100:1 primary-to-secondary impedance ratio.
How does transformer voltage ratio relate to impedance ratio?
The voltage ratio is Vp/Vs = a, while the impedance ratio is Zp/Zs = a².
How does transformer current ratio relate to impedance ratio?
With a = Np/Ns, the current ratio is Is/Ip = a. Combining voltage and current scaling gives Zp/Zs = a².
Does an ideal transformer change power?
No. The ideal transformer changes voltage, current, and referred impedance, but apparent power is conserved.
Can I use resistance values in this calculator?
Yes. A pure resistance is an impedance with zero phase angle, so speaker and load resistance examples are valid impedance magnitudes.
Can I use complex impedance?
The ideal formula also applies to complex impedance as Zp = a²Zs, but this V1 calculator accepts positive impedance magnitude only.
Does transformer impedance reflection change phase angle?
An ideal transformer with real positive turns ratio multiplies complex impedance by positive a², so it does not change phase angle.
Does frequency affect impedance transformation?
The ideal turns-ratio reflection formula does not require frequency. Real transformer input impedance can vary strongly with frequency because of magnetizing inductance, leakage, core loss, and parasitics.
Why does a real transformer input impedance differ?
Real transformers include winding resistance, leakage inductance, magnetizing branch, core loss, coupling limits, saturation, and frequency-dependent parasitics.
What is magnetizing impedance?
Magnetizing impedance is the no-load excitation branch associated with the transformer core. TRF-002 does not calculate it; TRF-010 owns magnetizing current scope.
Does this calculator include leakage inductance?
No. Leakage inductance is a real transformer parasitic and is outside this ideal impedance-ratio calculator.
Can this be used for audio transformers?
Yes, for first-pass ideal load reflection such as an 8 ohm speaker reflected to a tube or amplifier primary impedance. Bandwidth, core, leakage, and power rating still require separate checks.
Can this be used for RF quarter-wave transformers?
No. RF quarter-wave transformers are transmission-line matching structures and remain in the RF category.
Can this calculator calculate turns ratio?
Yes, in required-ratio mode it calculates a = sqrt(Zp/Zs). TRF-001 remains the main turns, voltage, and current ratio calculator.
What is the difference between TRF-001 and TRF-002?
TRF-001 calculates turns, voltage, and current ratio relationships. TRF-002 calculates impedance square-law reflection using the same a = Np/Ns convention.
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Related Engineering Resources
Guides and lookup references linked to this tool.
Engineering Guide
Transformer Impedance Matching: Turns Ratio, Reflected Load, Bandwidth, and Verification
Design transformer impedance matching using turns ratio, reflected complex load, source and load reference planes, bandwidth, losses, and measurement.
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Engineering Guide
Transformer Fundamentals: Turns Ratio, Impedance, Reflected Load, and Winding Connections
Learn transformer ratio conventions, voltage and current relationships, VA loading, impedance reflection, voltage regulation, and winding connection boundaries.
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