GHz to kHz for PLL Channel Steps and Divide Ratios

Sizing a Synthesizer Between a Gigahertz VCO and a Kilohertz Channel Step

A phase-locked loop is where two very different scales meet. The voltage-controlled oscillator is described in gigahertz, the channel step and the comparison frequency are described in kilohertz, and the divide ratio that ties them together is simply one divided by the other. Get that ratio wrong and every downstream number moves: in-band phase noise, lock time, the loop filter component values and where the spurs land.

Conversion factor: one gigahertz equals 1 000 000 kilohertz, so multiply the GHz figure by a million. A 2.4 GHz oscillator is 2 400 000 kHz, and with a 25 kHz channel step an integer-N loop needs a divide ratio of 2 400 000 ÷ 25 = 96 000.

What the ratio decides for you

The Step Dictates the Comparison Rate

In a classic integer-N architecture the phase detector must run at the channel step itself. Asking for 25 kHz channels means the detector compares only 25 000 times a second, however fast the oscillator behind it runs.

N Amplifies the Detector Noise

Noise at the phase detector reaches the output multiplied by twenty times the logarithm of N. At N = 96 000 that is a penalty of about 99.6 dB, which is why a large ratio shows up as a raised close-in noise pedestal.

A Slow Comparison Means a Slow Loop

A loop cannot be faster than the rate at which it is updated. With a 25 kHz comparison the usable loop bandwidth sits nearer 1–2.5 kHz, and lock time stretches accordingly.

Working Out a Divide Ratio While the Spec Is Still Open

Put the oscillator's top frequency in first

Type 2.4 into the gigahertz field and read 2 400 000 on the kilohertz side. Six zeros are easy to miscount by hand; the digits are grouped in threes here, so a factor of ten cannot hide in the middle of the number.

Divide by the channel step in your head

Once both quantities are in kilohertz the ratio is a plain division: 2 400 000 over 25 gives 96 000, and over 12.5 it gives 192 000. That number is what you enter in a register calculator and what your phase-noise budget hangs on.

Take the digits into the loop filter calculation

The copy button returns the bare figure with no unit and no display spacing, ready to drop into a charge-pump or loop-filter worksheet where a stray space would break the cell. Ctrl+C inside a field behaves the same way.

Turn a step size back into a tuning range

To check how far 96 000 steps of 25 kHz actually reach, work the other direction: type the kilohertz total, or press the swap arrows, and the gigahertz side answers. A comma decimal is accepted, which helps when the datasheet came from a European vendor.

Oscillator Outputs, Channel Steps and the Ratios They Force

Each row is a plausible synthesizer specification. The final column shows the in-band noise penalty that comes with the divide ratio, which is usually what pushes a designer from an integer-N loop towards a fractional one.

Oscillator output	Same value in kHz	Channel step	Integer-N ratio	20 log N penalty
1.2 GHz	1 200 000 kHz	12.5 kHz	96 000	99.6 dB
1.8 GHz	1 800 000 kHz	200 kHz	9 000	79.1 dB
2.4 GHz	2 400 000 kHz	25 kHz	96 000	99.6 dB
2.45 GHz	2 450 000 kHz	1 000 kHz	2 450	67.8 dB
3.5 GHz	3 500 000 kHz	100 kHz	35 000	90.9 dB
5.8 GHz	5 800 000 kHz	5 000 kHz	1 160	61.3 dB

Six Zeros You Do Not Have to Count

Grouped thousands keep 2 400 000 apart from 240 000 on sight, which is the single easiest way to put a decade of error into a divide ratio.

Step Size and Tuning Range in One Pair

Because both boxes accept input, the same pair answers how many kilohertz an oscillator spans and how many gigahertz a run of channel steps covers.

Fractional Steps Keep Their Decimals

Half-step grids such as 12.5 kHz survive intact, and up to eight decimal places are shown, so a non-integer ratio is visible rather than silently rounded.

Loop Design Questions Behind the Numbers

Why does the channel step set the comparison frequency in an integer-N loop?

Because the only knob available is an integer. If the feedback divider can be 96 000 or 96 001 and nothing in between, the output can only move by one comparison frequency at a time — so the comparison frequency and the channel step are the same number by construction. Wanting 25 kHz channels therefore forces a 25 kHz phase detector rate, which usually means dividing a 10 or 25 MHz reference down first. Everything unattractive about a fine grid follows from that one constraint rather than from the oscillator itself.

When is fractional-N worth its extra complexity?

As soon as a fine grid is costing you noise or lock time. A fractional divider dithers between N and N+1 so the average ratio is fractional, which frees the comparison frequency from the channel step entirely. Comparing at a 25 MHz reference instead of 25 kHz drops the ratio for a 2.4 GHz output from 96 000 to 96, and the 20 log N penalty from about 99.6 dB to about 39.6 dB — roughly 60 dB of in-band phase noise recovered, with a much wider loop bandwidth and far quicker settling. The price is quantisation noise from the modulator and fractional spurs at offsets that are not multiples of the reference, which is why integer-N still wins for a coarse grid or a very quiet fixed tone.

How large does the divide ratio become at gigahertz outputs with kilohertz steps?

Larger than most people guess before they convert the units. Land-mobile grids of 12.5 and 25 kHz applied to a low-gigahertz oscillator give ratios approaching six figures: 1.2 GHz over 12.5 kHz is 96 000, and 2.4 GHz over 25 kHz is the same 96 000. Numbers that size need a prescaler and a dual-modulus arrangement rather than a plain counter, and they push the in-band noise floor up by nearly a hundred decibels. Coarser grids look completely different — a 5 MHz step on a 5.8 GHz oscillator is only 1 160.

Where should the loop bandwidth sit relative to the comparison frequency?

Well below it — a tenth of the comparison rate is the usual ceiling and a twentieth is the safer working figure, so a 25 kHz comparison suggests a loop bandwidth somewhere between about 1.25 and 2.5 kHz. A sampled loop simply becomes unstable as its bandwidth approaches the rate at which it is updated, and a filter too close to the comparison frequency also fails to suppress the reference feedthrough. The other half of the choice is noise: inside the loop bandwidth the reference and detector dominate, outside it the oscillator does, so the crossover should ideally sit where those two curves meet.

At what offsets do reference spurs appear around the carrier?

At integer multiples of the comparison frequency on both sides of it. With a 25 kHz comparison, look at ±25, ±50 and ±75 kHz from a 2 400 000 kHz carrier; a 200 kHz comparison moves them out to ±200 kHz and beyond. They come from charge-pump mismatch and leakage modulating the tuning line once per comparison cycle, so the cures are matching and leakage control at the pump, plus enough attenuation at that offset in the loop filter. Their placement is also a diagnostic — a spur pair sitting exactly at the comparison spacing points at the reference path, while spurs at odd fractional offsets point at a fractional modulator instead.