The problem with a plain resistive divider is that the detector (or, in
the case of a scope probe, the scope input) invariably has an associated
shunt C. Without compensation, the lower arm of the divider gets less
voltage than it should, due to that shunt C. If the capacitive reactance
is high compared to the resistance of the lower divider arm at the
highest frequency of interest, then you can probably get by without
shunt capacitors. But otherwise, you need to make a compensated
attenuator by putting C across at least the upper divider arm.

The rule for making a compensated divider is that the time constants of
the top and bottom should be equal. That is, R1C1 = R2C2 where R1 and C1
are the parallel R and C at the bottom of the divider, and R2 and C2 at
the top.

This kind of divider has a theoretically flat frequency response, that
is, the voltage at the tap is constant assuming that the voltage applied
to the top of the divider is constant. But there's the rub. The
impedance of the divider is *not* constant with frequency -- because of
the C, it decreases as frequency increases. So depending on the circuit
it's put across, above some frequency the divider will begin disturbing
the circuit being measured due to the divider's too-low impedance.
Consequently, the design procedure is usually to first minimize the
detector or load C. This allows you to use the smallest possible C in
the top part of the divider, resulting in minimized loading of the
circuit to be measured. In general, you don't want to add physical C to
the lower part of the divider, unless the load (detector) C is variable,
unpredictable, or nonlinear, which requires it to be swamped by a known,
fixed, good-quality C.

Even such a simple circuit isn't trivial, if very accurate division and
wide frequency response (or fast and low-aberration time response) are
required. "Hook", "soak", and other nonlinear effects are well-known to
designers of oscilloscope front ends, as are the tricks and skills
necessary to avoid them. But these problems are much worse for high
impedance dividers than ones designed to operate in a low impedance
environment like 50 ohms.

Roy Lewallen, W7EL

gudmundur wrote:

Resistive dividers don't work worth a crap at rf, unless you use
non-inductive resistors, and then you must consider that your input
to the squaring circuit will have some capacitance to ground, who's
ability to screw up your higher frequency readings will be astronomical.
Why the squaring circuit?

Bottom line is this, all the resistive ladders I have played with
were worthless unless they contained capacitive compensation, which
can be found only by trial and error. I prefer a 'T' connection with
a good quality 'coaxial pad' of 10 db, then I feed it to my Tek 2215A
scope. It's deadly accurate from D.C. to at least 30mhz. More accurate
than any of my inline wattmeters, with the exception of the 'BIRD', and
that is only good across the spectrum of the slug I use.