STM32 PWM任意频率计算

以STM32F103为例总频是72M，定时器频率F与分频PSC、重装值ARR之间的关系为：

$$F=\frac{72M}{(ARR+1)\ast (PSC+1)}$$

如果是要根据频率F来计算ARR和PSC，由于ARR和PSC寄存器只有16位，所以ARR和PSC值都必须小于65535，且只能是整数，最简单的办法就是：
$$ARR=\sqrt[2]{72000000/F}-1$$
$$PSC=ARR$$
然后PSC和ARR都取整数部分，这样虽然简单快速，但是会存在一个问题，那就是很多频率F代入$\sqrt[2]{72000000/F}$计算出来的结果都含有小数，如果小数位是0.99，ARR和PSC取整后定时器输出跟计划的频率F有不小的误差，有些频率越高误差会越明显。如下的代码中的计算方式尽量计算出误差最小的ARR和PSC（以TIM1为例，输出PWM方便示波器查看）：

// 输入参数f就是PWM的输出频率
void TIM1_PWM_Init(uint16_t f)
{
	GPIO_InitTypeDef  			 GPIO_InitStructure;
	TIM_TimeBaseInitTypeDef  TIM_TimeBaseStructure;
	TIM_OCInitTypeDef  			 TIM_OCInitStructure;
	
	// 计算最合适的分频和重装值-------------------------------------------
	uint32_t period,prescaler;
	float midFloat,clkFloat ;
	long clkInt;
	long midInt;
	clkFloat = 72000000.0f/f;
	if(clkFloat-(long)clkFloat>=0.5f)  		clkInt = clkFloat+1;
	else							 		clkInt = (long)clkFloat;
	
	midFloat = sqrt(clkFloat);// 开方
	if(midFloat-(long)midFloat>=0.5f)  		midInt = (long)midFloat+1;
	else									midInt = (long)midFloat;
	// 找一组最接近的
	for(int i=midInt;i>=1;i--)
	{
		if(clkInt%i==0)
		{
			prescaler = i;
			period = clkInt/i;
			break;
		}
	}
	//-------------------------------------------------------------------
	// 以下是初始化TIM1的4个PWM输出通道
	RCC_APB2PeriphClockCmd(RCC_APB2Periph_GPIOA, ENABLE);
	GPIO_InitStructure.GPIO_Pin = GPIO_Pin_8 | GPIO_Pin_9 | GPIO_Pin_10 | GPIO_Pin_11;
	GPIO_InitStructure.GPIO_Mode = GPIO_Mode_AF_PP;
	GPIO_InitStructure.GPIO_Speed = GPIO_Speed_10MHz;
	GPIO_Init(GPIOA, &GPIO_InitStructure);

    RCC_APB2PeriphClockCmd(RCC_APB2Periph_TIM1, ENABLE);

	TIM_TimeBaseStructure.TIM_RepetitionCounter = 0;   // 这一行不加会导致输出延迟
	TIM_TimeBaseStructure.TIM_Period = period-1;
	TIM_TimeBaseStructure.TIM_Prescaler = prescaler-1;
	TIM_TimeBaseStructure.TIM_ClockDivision = TIM_CKD_DIV1;
	TIM_TimeBaseStructure.TIM_CounterMode = TIM_CounterMode_Up;
	TIM_TimeBaseInit(TIM1, &TIM_TimeBaseStructure);

	TIM_OCInitStructure.TIM_OCMode = TIM_OCMode_PWM1;
	TIM_OCInitStructure.TIM_OutputState = TIM_OutputState_Enable;
	TIM_OCInitStructure.TIM_OutputNState = TIM_OutputNState_Disable;
	TIM_OCInitStructure.TIM_Pulse = period/2;			// 50%占空
	TIM_OCInitStructure.TIM_OCPolarity = TIM_OCPolarity_High;
	TIM_OCInitStructure.TIM_OCNPolarity= TIM_OCPolarity_High;
	TIM_OCInitStructure.TIM_OCIdleState = TIM_OCIdleState_Reset;
	TIM_OCInitStructure.TIM_OCNIdleState = TIM_OCIdleState_Reset;
	
	TIM_OC1Init(TIM1, &TIM_OCInitStructure);
	TIM_OC1PreloadConfig(TIM1, TIM_OCPreload_Enable);

	TIM_OC2Init(TIM1, &TIM_OCInitStructure);
	TIM_OC2PreloadConfig(TIM1, TIM_OCPreload_Enable);

	TIM_OC3Init(TIM1, &TIM_OCInitStructure);
	TIM_OC3PreloadConfig(TIM1, TIM_OCPreload_Enable);
	
	TIM_OC4Init(TIM1, &TIM_OCInitStructure);
	TIM_OC4PreloadConfig(TIM1, TIM_OCPreload_Enable);

	TIM_ARRPreloadConfig(TIM1, ENABLE);
	TIM_CtrlPWMOutputs(TIM1, ENABLE);
	TIM_Cmd(TIM1, ENABLE);
}

（如果有更好的计算方式或者上面有什么不妥的地方请留言交流学习）