With AM transmitters, the information is in the change of the amplitude of the HF signal. Until the advent of transmitters based on switching technology (class D etc.), there were two versions of AM transmitters, depending on where the modulation was performed. If AM modulation is performed at a low HF signal level, and the modulated signal is then amplified, that output amplifier must be linear, and cannot operate in class C.
If modulation is performed at the output stage, this stage can operate in class C, provided that the modulator amplifier must be linear. It should not be forgotten that only the modulation amplifier should have IIRC a power of approximately 50% of the output power, so for an output power of eg 1kW, a linear power amplifier of 500W should be used for modulation. This modulator amplifier actually modulates the DC power supply for the output stage. When electronic tubes were used for this job, often the same type of tube was used for the output stage and for the modulator, so in the datasheets you will find characteristics for both C and B or AB class operation.
View attachment 94390
With FM transmitters, the information is in the frequency change, so class C output amplifiers can be used without any problems. Amplifiers in this class have a constant value of the amplitude of the HF signal output, often tightly limited.