# Calculating Gain for Audio Amplifiers

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1 Application eport SLOA105A October 003 evised September 005 Calculating Gain for Audio Amplifiers Audio Power Amplifiers ABSTACT This application report explains the different types of audio power amplifier configurations, such as the singleended (SE), the bridgetied load (BTL) and the fully differential audio amplifier. Each configuration is illustrated with a block diagram, gain equations, and an example using realistic scenarios to illustrate to engineers how to calculate the gain of their audio amplifier. Contents 1 ntroduction Power nto a Speaker Speaker mpedance Gain Setting for the Audio Power Amplifier... The SingleEnded (SE) Audio Power Amplifier Design...3. Equation SE Example The BridgeTied Load (BTL) Audio Power Amplifier Design Equation BTL Example The Fully Differential Audio Power Amplifier Design Equation Fully Differential Example Conclusion...13 Figures Figure 1. The SE Audio Power Amplifier...3 Figure. The SE Audio Power Amplifier Example...5 Figure 3. The BTL Audio Power Amplifier...6 Figure 4. The BTL Audio Power Amplifier Example...8 Figure 5. The Fully Differential Audio Power Amplifier...9 Figure 6. Output Power vs Supply Voltage Graphs for the TPA603A Figure 7. The Fully Differential Audio Power Amplifier Example

2 1 ntroduction The most common type of question that engineers ask when designing with audio power amplifiers is what gain should use? or, in other words, what resistor values should choose? This application report is broken up into three sections with gain calculations for: The SingleEnded (SE) Audio Power Amplifier The BridgeTied Load (BTL) Audio Power Amplifier The Fully Differential Audio Power Amplifier 1.1 Power nto a Speaker Before discussing the various audio power amplifier configurations, some basics about output voltage, speaker impedance and output power are presented. 1. Speaker mpedance n the case of audio power amplifier design, most speaker impedances are in the range of 3 Ω and 3 Ω, determined by whether it is driving a notebook, flat panel, cell phone speaker, or a headphone. Output voltage (V O ) is always specified as MS values, so for this application report, the following equation is used: Output Power where, [V O(MS) ] (PO ) = Load mpedance ( L ) V O(MS) = V O(PP) t is important to understand the relationship between peaktopeak output voltage, V O(PP), and the MS output voltage V O(MS), because this impacts the gain calculations of the audio power amplifier. 1.3 Gain Setting for the Audio Power Amplifier t is also imperative to understand that the output signal from the CODEC or DAC driving the audio power amplifier should be as large as possible, to have a high SN. Conversely, the gain of the audio power amplifier is set as low as possible. f the audio power amplifier s gain is set too high, then it amplifies the noise floor, along with the actual wanted signal of the CODEC or DAC. This decreases the dynamic range of the signal and reduces the quality of the sound. Calculating Gain for Audio Amplifiers

3 The SingleEnded (SE) Audio Power Amplifier.1 Design The SE amplifier is the simplest type of configuration and is used either when driving headphones, or when using a split voltage supply. Figure 1 illustrates the block diagram for such an amplifier. F nput Signal C C OUT A V DD / LOAD C BYPASS Figure 1. The SE Audio Power Amplifier. Equation As illustrated in Figure 1, this type of amplifier has an inverting amplifier providing the gain. The input resistor,, and the feedback resistor, F, provide the voltage gain of the amplifier in the following relationship: Gain = F (Output signal is 180 O out of phase, versus the input signal) Therefore, for a voltage gain of 10 V/V or 0 db, F is 10 times larger than. Typical value for these resistors would be = 10 kω and F = 100 kω. The following is an example for the gain calculation for a SE audio power amplifier. Calculating Gain for Audio Amplifiers 3

4 .3 SE Example Questions: An engineer s design requires 100 mw of MS output power to be driven into his 16Ω speaker. The audio amplifier runs off a 5V supply and is driven by an audio CODEC that has a maximum (peaktopeak) output voltage of 3 V. What must the gain of the amplifier be to ensure that the amplifier can delivery the required power into the load and what values of resistors should be used? Answer: Starting from the output power requirements, first, calculate the voltage across the load that allows 100 mw to drive the speaker. Using the following equation, [Output Voltage(V O(MS) )] Output Power (P O ) = Load mpedance ( L ) [V O(MS) ] 100 mw =, therefore, 16 Ω V O(MS) = 0.1x 16, which means that the MS output voltage, V O(MS), from the audio power amplifier is 1.6 V. Because the peaktopeak output voltage of the CODEC is 3 V, convert this to MS voltage, VO(PP) VO(MS) =, substituting in the number from this example, 3 V O(MS) = = 1.06 V. Therefore, the MS output voltage from the CODEC is 1.06 V and the MS output voltage needed from the amplifier is 1.6 V. The gain of the amplifier is 1.18 V/V or 1.4 db. Using Equation 3, as illustrated earlier, Gain = F, substituting in the numbers from this example, F = This means that is 10 kω and F is 11.8 kω. This results in the following block diagram illustrated in Figure. 4 Calculating Gain for Audio Amplifiers

5 11.8 kω nput Signal 0.1 µf 10 kω 68 µf V DD / A 16 Ω 1 µf Figure. The SE Audio Power Amplifier Example Note: The input coupling capacitor, C, and the input resistor,, form a highpass filter with a cutoff frequency, f C, at: 1 f C = x π x C x The value of C and should be carefully chosen to ensure that the highpass filter does not attenuate the wanted audio frequencies. n this example, setting the input capacitor to 0.1 µf results in a cutoff frequency of 169 Hz. This also applies to the output dc blocking capacitor, because this, together with the speaker impedance, also creates a highpass filter. Choose the value of the dc blocking capacitor ensuring that the low audio frequencies are not attenuated. 1 f C = x π x C OUT x LOAD n this example, with the output capacitor, C OUT, set at a value of 68 µf, the resultant cutoff frequency is 146 Hz, so that it is close to the cutoff frequency of the input highpass filter. Calculating Gain for Audio Amplifiers 5

6 3 The BridgeTied Load (BTL) Audio Power Amplifier 3.1 Design The BTL configuration differs from the SE configuration in that it includes an inverter follower to double the voltage across the load. This type of audio power amplifier is used when using a single supply voltage and maximizing the power to the load from that single supply. Figure 3 illustrates the block diagram for such an amplifier. V DD / F nput Signal C A C BYPASS LOAD B Figure 3. The BTL Audio Power Amplifier As illustrated in Figure 3, this type of amplifier has the same inverting amplifier that provided the gain for the SE amplifier, but an inverter follower has been added to invert the output signal from the gaining amplifier, hence, doubling the voltage across the load. This results in a quadrupling of the power to the load, compared to the SE configuration mentioned previously. 3. Equation The input resistor and the feedback resistor F still provide the voltage gain of the amplifier. But in the case of the BTL amplifier, relationship has changed to: Gain = F (Output signal is 180 O out of phase, versus the input signal) Therefore, for a voltage gain of 10 V/V or 0 db, F must only be 5 times larger than. Following is an example for the gain calculation for a BTL audio power amplifier. 6 Calculating Gain for Audio Amplifiers

7 3.3 BTL Example Question: An engineer s design requires that W of MS output power be driven into his 4Ω speaker. The audio amplifier runs off a 5V supply and is driven by an audio CODEC that has a maximum (peaktopeak) output voltage of 3 V. What must the gain of the amplifier be to ensure that the amplifier can deliver the required power into the load, and what values of resistors should be used? Answer: Starting from the output power requirements, the first thing to do is to calculate the output voltage across the load that allows W to drive the speaker. Using the following equation, Output Power (P ) O = [Output Voltage(V [V O(MS) ] W =, therefore, 4 Ω Load mpedance ( O(MS) L )] ) V O(MS) = x 4, which means that the MS output voltage from the audio power amplifier must be.83 V. Because the peaktopeak output voltage of the CODEC is 3 V, convert this to MS voltage, VO(PP) VO(MS) =, substituting in the numbers from this example, 3 V O(MS) = = 1.06 V. Therefore, the MS output voltage from the CODEC is 1.06 V and the MS output voltage needed from the amplifier is.83 V. The gain of the amplifier must be.67 V/V or 8.5 db. Using Equation 4, as illustrated earlier, Gain = F, substituting in the number from this example, F = This means that is approximately 10 kω and F is approximately 13.3 kω. This results in the following block diagram illustrated in Figure 4. Calculating Gain for Audio Amplifiers 7

8 V DD / 13.3 kω nput Signal 0.1 µf 10 kω A 1 µf 4 Ω B Figure 4. The BTL Audio Power Amplifier Example Note: The input coupling capacitor, C, and the input resistor,, form a highpass filter. The values of C and should be chosen to ensure that the highpass filter does not attenuate the wanted audio frequencies. n this example, the input capacitor is set to 0.1 µf to provide a cutoff frequency of 169 Hz. Note that in Figure 4, the dc blocking capacitor used in the SE configuration has been omitted. Because both outputs are biased to the same dc voltage and the speaker is no longer referenced to ground, the dc blocking capacitor is no longer required. Only the input capacitor and resistor limit the low frequency response of the system. 8 Calculating Gain for Audio Amplifiers

9 4 The Fully Differential Audio Power Amplifier 4.1 Design The fully differential configuration is very different from the typical BTL configuration. There is no inverterfollower to double the voltage across the load. However, because this is a differential amplifier, the output power to the load is the same as for the typical BTL amplifier, with the benefit that it is more immune to noise, both on the inputs and the outputs. This type of audio power amplifier maximizes the power to the load from a single supply in a similar way to the typical BTL amplifier mentioned earlier and performs very well in noisy environments, such as a cell phone or smart phone. Figure 5 illustrates the block diagram for such an amplifier. nput Signal F LOAD nput Signal F Figure 5. The Fully Differential Audio Power Amplifier As illustrated in Figure 5, this amplifier consists of a fullydifferential amplifier that provides the gain. As mentioned previously, the differential voltage swing across the load, results in a quadrupling of the power to the load, as in the case of the typical BTL amplifier. 4. Equation The input resistor and the feedback resistor F still provide the voltage gain of the amplifier. But in the case of the fully differential amplifier, the relationship has changed to: Gain = F Therefore, for a voltage gain of 10 V/V or 0 db, F only must be 10 times larger than. Following is an example for the gain calculation for a fully differential audio power amplifier. Calculating Gain for Audio Amplifiers 9

10 4.3 Fully Differential Example Questions: An engineer s design requires the maximum MS power from the TPA603A1 be driven into a standard 8Ω speaker while keeping the THDN less than 10%. The audio amplifier runs off a battery that varies from 4. V down to 3 V. The input to the amplifier is an audio CODEC that has a maximum (peaktopeak) output voltage of 1.8 V. What gain should be used to ensure that the TPA603A1 can deliver the maximum power into the load while keeping the THDN less than 10%? Answer: First, calculate the output power at 10% THDN at 3V supply. t is important to choose the minimum supply voltage, because, if calculating the gain at a 4.V supply, and the battery drops to 3 V, then it is likely that the output signal for the amplifier will clip and cause higher THDN than originally expected. Obtain the required output power from the Output Power versus Supply Voltage graph illustrated in Figure 6, which at 10% THDN and 3V supply is 550 mw. P O Output Power W L =8Ω f=1khz Gain = 1 V/V OUTPUT POWE vs SUPPLY VOLTAGE THDN = 10% THDN = 1% V DD Supply Voltage V Figure 6. Output Power vs Supply Voltage Graphs for the TPA603A1 Once the output power has been determined, calculating the required output voltage of the amplifier is done as in the previous sections using the following equation: 10 Calculating Gain for Audio Amplifiers

11 Output Power (P ) O = [Output Voltage(V [V O(MS) ] 0.55 W =, therefore 8 Ω Load mpedance ( O(MS) L )] ) V O(MS) = 4.4 be.10 V., which means that the MS output voltage from the audio power amplifier must Because the peaktopeak output voltage of the CODEC is now 1.8 V, convert this to MS voltage, V O(MS) = V O(PP) 1.8 V O(MS) = = 0.64 V, substituting in the numbers from this example Therefore, the MS output voltage from the CODEC is 0.64 V and the MS output voltage needed from the amplifier is.1 V. The gain of the amplifier will be 3.8 V/V or 10.3 db. Using Equation 5, as illustrated earlier, Gain = F, substituting in the number from this example, F = 3.8. This means that is 10 kω and F is approximately 3.8 kω. ealizing that 3.8 kω is not a standard value, the nearest value available should be 33. kω. This results in the following block diagram: nput Signal 10 kω 33. kω 8 Ω nput Signal 10 kω 33. kω Figure 7. The Fully Differential Audio Power Amplifier Example Calculating Gain for Audio Amplifiers 11

12 Note: n the case that F is integrated into the amplifier, which is typical of good audio power amplifiers, then obviously F is set to whatever value is in the data sheet and is chosen to provide the necessary gain. The resistors also typically need to be matched to 1% or better, because the better the matching of these components, then the better the power supply rejection ratio (PS) of the amplifier. 1 Calculating Gain for Audio Amplifiers

13 5 Conclusion n calculating the gain of an audio power amplifier, it is important to ensure that the correct MS values are used when calculating the necessary gain for the amplifier. t is also important to note, that when using input or output coupling capacitors, a highpass filter is formed., C or C OUT should be chosen to ensure that the wanted audio frequencies are passed through this filter. Calculating Gain for Audio Amplifiers 13

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