MT-076 tutorial differential driver analysis differential drivers can be driven by either sing le-ended or differential signals. this tutorial analyzes both conditions using either an unterminated or a terminated source. case 1: differential input, unterminated source figure 1 shows a differential driver driven from a balanced unterminated source. this would typically be the condition for a low impedance s ource where the connection distance between the source and the driver is minimal. r f1 r f2 r g1 r g2 v ocm v out + ? + ? r s / 2 v sig / 2 v sig / 2 r s / 2 v icm + + ? ? r g1 = r g2 r f1 = r f2 v out+ v out? 2/rr r v vv v v g s1g 1f sig out out in out + = ? == ? + v in figure 1: differential input, unterminated source the design inputs are th e source impedance r s , the gain setting resistor r g1 , and the desired gain g. note that the gain is measured with respect to the signal voltage source, v sig . the total value of the gain setting resist or with respect to the signal source, v sig , is r g1 + r s /2. also, r g2 = r g1 . the required value of the feedback resistors, r f1 = r f2 , is then calculated using: ? ? ? ? ? ? +== 2 r rgrr s 1g 2f1f eq. 1 rev.0, 10/08, wk page 1 of 9
MT-076 case 2: differential input, terminated source there are many cases where the differential driv ing source drives a twisted pair cable which must be terminated in its characteristic impedance to maintain high bandwidth and minimize reflections as shown in figure 2. r f1 r f2 r g1 r g2 v ocm v out + ? + ? r s / 2 v sig / 2 r t v sig / 2 r s / 2 v icm r in = r g1 + r g2 = 2r g1 + + ? ? r g1 = r g2 r f1 = r f2 v d+ v d? 1g 1f dd out out in out r r vv vv v v g = ? ? == ?+ ? + v out+ v out? v in figure 2: differential input, terminated source the design inputs are th e source impedance r s , the gain setting resistor r g1 , and the desired gain g. note that for the terminated case, the gain is measured with respect to the differential voltage at the termination, v in = v d+ ? v d? . the input impedance, r in , is equal to 2r g1 for a balanced differential drive. the termination resistor, r t , is selected so that r t ||r in = r s , or 1gs t r2 1 r 1 1 r ? = eq. 2 the required value of the feedback resistors, r f1 = r f2 , is then calculated using: r f1 = r f2 = g ? r g1 eq. 3 page 2 of 9
MT-076 case 3: single-ended inpu t, unterminated source there are many applications where a differentia l amplifier provides an effective means of converting a single-ended signal into a differential one. figur e 3 shows the case of an unterminated single-ended driver. r f2 r g1 r g2 r s v ocm v sig v out + ? + ? r f1 r g2 = r g1 + r s r f1 = r f2 s1g 1f sig out out sig out rr r v vv v v g + = ? == ? + v out+ v out? figure 3: single-ended i nput, unterminated source the design inputs are th e source impedance r s , the gain setting resistor r g1 , and the desired gain g. note that the gain is measured with respect to the signal voltage source, v sig . in order to prevent v ocm from producing an unwanted offset voltage at the di fferential output, the net impedances seen by both i nputs of the differential amplifie r must be equal. therefore, r g2 = r g1 + r s eq. 4 the value of the feedback resistor s is then calculated using: r f1 = r f2 = g(r g1 + r s ) eq. 5 page 3 of 9
MT-076 case 4: single-ended inpu t, terminated source figure 4 shows a very common app lication where a single-ended s ource drives a coaxial cable which must be properly terminated to minimi ze reflections and main tain high bandwidth. the design inputs are th e source impedance r s , the gain setting resistor r g1 , and the desired gain g. note that the gain is measured with r espect to the voltage at the termination, v in . r f2 r g1 r g2 r s v ocm v sig v out + ? + ? r f1 r t v in v out+ v out? in out out in out v vv v v g ? + ? == )rr(2 r 1 r r 1f1g 1f 1g in + ? = r g2 = r g1 + r s ||r t r f1 = r f2 z in = r in ||r t figure 4: single-ended input, terminated source knowing the desired gain, g, the gain-setting resistor r g1 , and the source resistance, r s , calculate the initial value of the feedback resistor, r f1a . the final value of this resistor will be slightly higher due to the increase in r g2 required to match input impedances. this will be included in later equations. the calculations proceed as follows: r f1a = g ? r g1 eq. 6 )rr(2 r 1 r r a1f1g a1f 1g in + ? = eq. 7 page 4 of 9
MT-076 ins t r 1 r 1 1 r ? = eq. 8 ts ts ts rr rr r + = eq. 9 r g2 = r g1 + r ts eq. 10 the input voltage v in can be related to the source voltage v sig by: ? ? ? ? ? ? + = sint int sigin r)r||r( r||r vv eq. 11 ? ? ? ? ? ? + = int sint insig r||r r)r||r( vv eq. 12 in order to calculate the final value of the fee dback resistors, the thev enin equivalent circuit shown in figure 5 is used. r f1 r f2 r g1 r g1 r s ||r t v ocm v in v out + ? + ? ? ? ? ? ? ? + st t sig rr r v r ts = r s ||r t r g2 = r g1 + r s ||r t r f1 = r f2 )rr(2 r 1 r r 1f1g 1f 1g in + ? = figure 5: thevenin equivalent input circuit page 5 of 9
MT-076 the output voltage can be e xpressed as a function of the source voltage as follows: ? ? ? ? ? ? ? ? ? ? ? ? + = 2g 2f st t sig out r r rr r vv eq. 13 substituting eq. 12 for v sig into eq. 13: ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? + = 2g 2f st t int sint in out r r rr r r||r r)r||r( vv eq. 14 ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? + == 2g 2f st t int sint in out r r rr r r||r r)r||r( v v g eq. 15 in the case of a proper termination, r s = r t ||r in , and eq. 15 reduces to: ? ? ? ? ? ? ? ? ? ? ? ? + = 2g 2f st t r r rr r2 g eq. 16 solving eq. 16 for r f2 = r f1 : ? ? ? ? ? ? + == t ts2g 1f2f r2 )rr(r grr eq. 17 common-mode input and ou tput considerations care must be taken in applying differential amplifiers to make su re the input and output common-mode voltage ranges are not exceeded. this is especially true in single-supply applications. figure 6 shows an application of a differentia l amplifier where a sing le-ended bipolar ground- referenced signal must be converted into a differen tial signal suitable for driving an adc. in this example, the common-mode input voltage of the adc is +2.5 v, and the differential input swing of the adc is 4 v p-p. many differential amp lifiers can handle the output swing provided the power supply is at least +5 v. page 6 of 9
MT-076 ? input cm voltage is a scaled replica of the input signal ? input cm voltage partially bootstraps rg, raising effective input resistance ? single-supply application can accept bipolar input ? must ensure that input common-mode voltage stays within specified limits v 5.2 2v 0v -2v 3.5 v 2.5v 1.5 v 3.5 v 2.5v 1.5 v 3.5 v 2.5v 1.5 v 3.5 v 2.5v 1.5 v 3.5 v 2.5v 1.5 v 3.5 v 2.5v 1.5 v 1.75 v 1.25 v 0.75 v 1.75 v 1.25 v 0.75 v 1.75 v 1.25 v 0.75 v + ? v out+ v out? 500 : 500 : 500 : 500 : + ? v ocm figure 6: input/output common-mode requirements for single-ended to differential c onverter with bipolar input signal the corresponding input signal sw ing at the (+) and (? ) amplifier terminals is also shown in figure 6. note that it is a scaled replica of th e input signal. the specific ations on the differential amplifier must allow for an input common-mode vol tage between +0.75 v and +1.75 v under these conditions. this is also possibl e with many differential amplifiers. figure 7 shows an application where a single-ended unipolar si gnal is converted with a differential amplifier. in this case, the common-mode output voltage is set for +2 v. the input signal swings from 0 v to +4 v. the corresponding signal swing on the amplifier input terminals is from +1.5 v to +2.5 v. the amplifier outputs must swing from +1 v to +3 v. the differential amplifier selected must be able to handle these requirements when operating on the desired supply voltage(s). the adisimdiffamp interactive design tool performs th ese input/output signal calculations for the various analog device's differential amplifie rs and greatly simplifies the selection process. error flags are generated if the signals fall outside the allo wable ranges on either the input or output. page 7 of 9
MT-076 v 2 4v 2v 0v 4v 2v 0v 3v 2v 1v 3v 2v 1v 3v 2v 1v 3v 2v 1v 2.5v 2v 1.5 v v 2 + 500 500 500 500 + ? v ocm + ? 0.1f 10f figure 7: input/output common-mode requirements for single-ended to differential con verter with unipolar input signal ac-coupled driver applications ac-coupled applications of differential drivers are straightforw ard. figure 8 shows a typical single-ended to differential ac-c oupled driver. note that the im pedances are balanced on each input in order to achieve the be st distortion performance. the lo w frequency cutoff of the input circuit is equal to: c1g c cr2 1 f = eq. 18 the value of c c should be chosen so that this fre quency is at least 10 times less than the minimum desired signal frequency. page 8 of 9
MT-076 r f2 r g1 r g1 r s v ocm v sig v out + ? + ? r f1 r t v in v out+ v out? r ts = r s ||r t r ts c c c c figure 8: typical ac-coupl ed driver application references 1. hank zumbahlen, basic linear design , analog devices, 2006, isbn: 0-915550-28-1. also available as linear circuit design handbook , elsevier-newnes, 2008, isbn-10: 0750687037, isbn-13: 978- 0750687034. chapter 2. 2. walter g. jung, op amp applications , analog devices, 2002, isbn 0-916550-26-5, also available as op amp applications handbook , elsevier/newnes, 2005, isbn 0-7506-7844-5. chapter 3. 3. walt kester, analog-digital conversion , analog devices, 2004, isbn 0-916550-27-3, chapter 6. also available as the data conversion handbook , elsevier/newnes, 2005, isbn 0-7506-7841-0, chapter 6. 4. walt kester, high speed system applications , analog devices, 2006, isbn-10: 1-56619-909-3, isbn-13: 978-1-56619-909-4, chapter 2. 5. adisimdiffamp , an analog devices' on-line interactive design tool for differential amplifiers. copyright 2009, analog devices, inc. all rights reserved. analog devices assumes no responsibility for customer product design or the use or application of customers? products or for any infringements of patents or rights of others which may result from analog devices assistance. all trad emarks and logos are property of their respective holders. information furnished by analog devices applications and development tools engineers is believed to be accurate and reliable, however no responsibility is assumed by analog devices regarding technical accuracy and topicality of the content provided in analog devices tutorials. page 9 of 9
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