Current Ratio
How Current Ratio Is Defined and Scaled
A current ratio is simply one current measured against a reference current, written as I2/I1. Because both quantities carry the same unit (amperes), the ratio itself is dimensionless. This makes it a convenient building block for describing transfer relationships across components that scale current rather than voltage: current transformers, current mirrors, current dividers, and the current-gain stage of a bipolar transistor. When two branches share a node, Kirchhoff's current law forces the branch currents to sum to the source current, and the current ratio between branches is set purely by their relative admittances.
The decibel form is where engineers most often trip up. Power in a fixed resistance is proportional to I2, so a current ratio maps to power-decibels through 20 log10 of the ratio, identical to the voltage-ratio rule and distinct from the 10 log10 rule reserved for direct power ratios. A 3 dB current change therefore corresponds to a factor of roughly 1.41, not 2. Applying the wrong factor of two doubles or halves every figure on a budget, so the convention matters when current transfer terms are folded into a cascaded gain or loss calculation.
At radio frequencies the current ratio of an active device is frequency dependent. The short-circuit current gain magnitude, h21, rolls off at 20 dB per decade and crosses unity at the transition frequency fT. Below fT the device delivers a usable current ratio greater than one; above it the current ratio drops below one and the transistor can no longer provide current gain, which is why fT is a headline figure of merit for RF transistors.
Governing Equations
AI = I2 / I1 (dimensionless)
Current ratio in decibels:
AI(dB) = 20 × log10(I2 / I1)
Current transformer:
Isec / Ipri = Npri / Nsec = 1 / n
Current divider (two branches):
I1 / Itotal = G1 / (G1 + G2) = R2 / (R1 + R2)
Where I = current (A), N = turns, n = turns ratio, G = conductance (S), R = resistance (Ω). Example: a 200:5 CT has n = 40, so 120 A primary → 3 A secondary, a current ratio of 0.025 or ≈ −32 dB.
Current Ratio in Common RF Contexts
| Context | What the ratio represents | Typical value | In dB (20 log) | Set by |
|---|---|---|---|---|
| Current transformer | Isec / Ipri | 0.01 to 0.2 | −40 to −14 dB | Turns ratio |
| Current divider | Branch I / total I | 0 to 1 | −∞ to 0 dB | Branch admittances |
| BJT current gain β | IC / IB | 50 to 300 | +34 to +50 dB | Device geometry |
| BJT alpha α | IC / IE | 0.98 to 0.995 | −0.18 to −0.04 dB | Base transport |
| RF current gain h21 | Iout / Iin (short circuit) | 1 at fT | 0 dB at fT | Frequency, fT |
Frequently Asked Questions
When is a current ratio expressed in decibels and which formula applies?
Use 20 log10(I2/I1), not 10 log10, because power scales with the square of current in a fixed resistance. A current ratio of 2 is +6.02 dB, 10 is +20 dB, and 0.5 is −6.02 dB. The 10 log rule applies only when the compared quantity is power. The same 20 log rule covers voltage ratios and reflection coefficients, so a current ratio in dB is directly comparable across the same impedance.
How does a current transformer turns ratio relate to its current ratio?
The secondary current equals the primary current divided by the turns ratio, so a 100:1 turns ratio gives a 100:1 current ratio and steps 100 A down to 1 A. It is the inverse of the device's voltage ratio. Real CTs deviate because of core magnetizing current: ratio error runs about 0.1 to 1 percent for metering cores and grows near the low end of the rated range and under burden or saturation.
What is the difference between current ratio and current gain in a transistor?
Current gain is a specific current ratio. For a BJT, β (hFE) is IC/IB, typically 50 to 300, and α is IC/IE, just under 1. Those are DC ratios. At RF the relevant figure is h21, which drops 20 dB per decade and reaches unity (current ratio 1, or 0 dB) at the transition frequency fT; useful gain exists only well below fT.