The Valve Wizard

A resistor is often placed in series with the signal before it reaches the grid of a valve. This is known as a 'grid-stopper' and serves several purposes.

It is usual place the grid-leak resistor before the grid-stopper. This will increase the total grid-leak resistance so be sure not to exceed the maximum rated value. Adding it after the grid-stopper will create a potential divider that will attenuate the input signal slightly, which is usually avoided, although may be necessary in some cases.

Frequency response and the Miller effect: Grid-stoppers can be used to control the high frequency roll-off response of amplfier stages.
On the input of an amp its function is to 'stop' radio frequencies (all those above 20kHz) from reaching the grid and causing unwanted interference. While this wouldn't damage the circuit, inaudible RF interference can damage tweeters, and you certainly don't want to hear your local radio station playing through your amp!
Wherever possible, the grid stopper should be soldered very close to, or directly onto the valve socket to maximise its effect, so that radio interference is less likely to be picked up on the wire between grid-stopper and valve grid.

The grid-stopper attenuates the RF by forming a low-pass RC filter with the valve's 'dynamic input capacitance'. This is the combination of the valve's static inter-electrode capacitances, plus the Miller capacitance.
The static inter-electrode capacitance is the product of all the internal capacitances within the valve, formed between the various metal parts. Miller capacitance is an effect produced within the valve (the Miller effect), such that the static grid-to-anode capacitance is actually multiplied by the gain of the stage. The static inter-electrode capacitances (those actually measured between valve pins), are quoted on the valve's data sheet, and the two most important are the grid-to-cathode (Cgk) and grid-to-anode capacitances (Cga), shown in red.
(Cgk may not be quoted, in which case the "grid to all except anode" capacitance should be used instead.)

The dynamic input capacitance (Cdyn) which you need to know when choosing a value for the grid stopper is:
Cdyn = Cgk + (Cga * A)
(Where: A = the voltage gain of the stage)

Using a typical ECC83 triode with a bypassed cathode as an example:
Cgk=1.6pF
Cga=1.6pF
A=60

Cdyn = 1.6 + (1.6 * 60)
= 97.6pF
The actual wiring within the amplifier will also have 'stray' capacitance, so it is usual to add a few extra pico-Farads to our answer to allow for this, making about 100pF in total.

To find a suitable value for the grid-stopper, simply apply the formula for a low-pass filter, where C is the dynamic input capacitance and f is the desired low roll-off frequency- in this case 20kHz:
Rg = 1 / (2 * pi * f * C)
Rg = 1 / (2 * pi * 20000 * (100 * 10-12))
= 79.6k
You will often see old amplifier designs using a 68k grid stopper. This will provide a roll-off of approximately 23kHz, which is close enough. However, the guitar itself also contributes a series resistance, that may range from a few kilo-ohms to several hundred kilo-ohms if the volume controls are turned down. This can easily cause treble frequenices to be rolled off, losing some of the high harmonics and 'chime' of the guitar sound. In practice it seems that in most cases the grid stopper can actually be made quite a bit smaller than 68k, and 10k to 33k will do, unless you happen to be playing nextdoor to a radio transmitter.

It is worth noting that in pentodes Cag is very small, so the dynamic input capacitance can be assumed to be roughly equal to Cgk.

Increasing Miller capacitance: A further problem with the usual approach is that it places a very large value resistor in the signal path, which introduces noise. This isn't a worry in later parts of the preamp, but at the input we want to keep it to the bare minimum.
The grid stopper can be made smaller in value if the effective value of the input capacitance is made proportionately larger. This can be done by placing a capacitor between the anode and grid of the valve. This capacitor applies negative feedback of very high frequencies to the grid, and appears in parallel with the Miller capacitance, so its value is also multiplied by the gain of the stage, due to the Miller effect. Therefore the effective input capacitance is greatly increased and becomes equal to:
Cin = Cgk + (Cga * A) + (Cf * A)
Or: Cin = Cdyn + (Cf * A)

To use the previous example, a roll-off of 20kHz is desired, but this time with a grid-stopper of just 10k. The necessary effective input capacitance required would be:
Cin = 1 / (2 * pi * 20000 * 10000)
= 796pF

The value of the feedback capacitor would therefore be:
Cf = (Cin - Cdyn) / A
(where Cdyn is 100pF found earlier)
= (796 - 100) / 60
=11.6pF
In this case the closest standard value would be 10pF, providing an acceptable roll-off of about 23kHz. The capacitor used should be of high quality so as not to introduce its own noise, and should have sufficient voltage tolerance to withstand the anode voltage. A close tolerance ceramic capacitor would suffice.

For those afraid of the capacitor failing and placing a high voltage on your guitar strings, the capacitor could be placed between grid and cathode instead, although it will need to be a higher value since it won't be subject to the Miller effect. In this case:
796 - 100 = 696pF
The closest standard would be 680pF.

The succeeding gain stages in an amplifier are normally enclosed within an earthed chassis where RF interference is unlikely to be picked up, therefore RF blocking is usually only used on the input where the guitar and guitar lead can act as antennae. However, if RF is getting into an amp somewhere, it may be necessary to add a grid stopper and/or feedback capacitor to the offending valve.

Of course, we don't just have to limit RF. Any roll-off frequency can be chosen for this method, and it is often used to limit treble frequencies in bright amplifiers, and this is why you may see grid-stoppers in later stages within an amplifier.

Other reasons for grid-stoppers: While the input of the amplifier will usually have a grid-stopper to remove radio interference, other stages in the amp- particularly the power valves- will often have grid-stoppers for different reasons.
The first is that the actual wiring inside the amp will have stray inductances. In combination with the input capacitance of a valve, this will produce a resonant circuit which can cause parasitic oscillation, particularly in high gm valves like power valves. This is cured by damping the resonance with a grid-stopper, fitted directly to the valve socket if possible. Data sheets will usually list a recommended value of grid-stopper, and typical values are around 1k to 10k on power valves. If in doubt, make it bigger. Most small signal valves don't suffer from this condition, although the ECC88 is an example of one that does.

The second reason is to limit grid current. In hifi this isn't such an important issue, but in a guitar amp the valves will often be driven well into grid-current territory. If left unchecked, this can cause the grid to exceed its ratings and be destroyed, although this is very rare.
The main reason for limiting grid-current is to reduce blocking distortion. By adding a grid-stopper, the input impedance of the stage cannot fall below the value of the grid-stopper. The maximum current that can flow in the grid is therefore limited, and the preceding stage cannot become so heavily loaded. By limiting the current we prevent the coupling capacitor from becoming fully charged during an overload, and therefore it can discharge faster once the overload has passed. Additionally, when current does start to flow during overload, the voltage drop across the grid-stopper will increase and so reduce the voltage on the grid countering, providing a voltage limiting effect as well as a current limiting one.
For a good, modern design, all valves should have grid stoppers, even if it a small value of around 10k say. Values up to 1Meg are quite reasonable though, and are a powerful tool in tweaking the overdrive and treble characteristics of the amp. Except for the input stage, the stopper does not need to be connected directly to the valve socket. Stages enclosed within a feedback loop (usually the output stage) are even more suseptible to blocking distortion so using large grid-stoppers will be even more necessary for these.

Screen-grid stoppers: The screen-grid on a power pentode should also have a grid-stopper to protect it from over dissipation when the valve is overdriven, which causes the screen-grid to draw more current. The voltage drop across the screen-stopper will reduce the screen voltage, hopefully saving the valve from destruction. The resistor is usually 1k in value and at least 1W, although higher wattages are more preferable.
On ultra-linear power stages a grid-stopper on the screen-grid is not absolutely necessary, although for peace of mind it can be fitted. In hifi a 47R resistor is often used for this as it supposedly reduces distortion, and you sometimes see a similar resistor placed at the anode (anode-stopper) to quell parasitic oscillation or reduce distortion.