STM32 PWM任意頻率計算

以STM32F103爲例總頻是72M，定時器頻率F與分頻PSC、重裝值ARR之間的關係爲：

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

如果是要根據頻率F來計算ARR和PSC，由於ARR和PSC寄存器只有16位，所以ARR和PSC值都必須小於65535，且只能是整數，最簡單的辦法就是：
$ARR=\sqrt[2]{72000000/F}-1$
$PSC=ARR$
然後PSC和ARR都取整數部分，這樣雖然簡單快速，但是會存在一個問題，那就是很多頻率F代入$\sqrt[2]{72000000/F}$計算出來的結果都含有小數，如果小數位是0.99，ARR和PSC取整後定時器輸出跟計劃的頻率F有不小的誤差，有些頻率越高誤差會越明顯。如下的代碼中的計算方式儘量計算出誤差最小的ARR和PSC（以TIM1爲例，輸出PWM方便示波器查看）：

// 輸入參數f就是PWM的輸出頻率
void TIM1_PWM_Init(uint16_t f)
{
	GPIO_InitTypeDef  			 GPIO_InitStructure;
	TIM_TimeBaseInitTypeDef  TIM_TimeBaseStructure;
	TIM_OCInitTypeDef  			 TIM_OCInitStructure;
	
	// 計算最合適的分頻和重裝值-------------------------------------------
	uint32_t period,prescaler;
	float midFloat;
	long clkInt;
	long midInt;
	clkFloat = 72000000.0f/f;
	if(clkFloat-(long)clkFloat>=0.5f)  		clkInt = clkFloat+1;
	else							 		clkInt = (long)clkFloat;
	
	midFloat = sqrt(clkFloat);// 開方
	if(midFloat-(long)midFloat>=0.5f)  		midInt = (long)midFloat+1;
	else									midInt = (long)midFloat;
	// 找一組最接近的
	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個PWM輸出通道
	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;   // 這一行不加會導致輸出延遲
	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%佔空
	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);
}

（如果有更好的計算方式或者上面有什麼不妥的地方請留言交流學習）