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mathcad做电路分析.pdf

发布时间：2022-06-13 发布人：admin 分类：说明书 资料大小：0.06M 资料格式：pdf 举报 版权申诉
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    ANALOG INPUT TO MICRO EXAMPLE Requirements Must be able to detect all four states from 9V to 16V battery Dedicated ground so ground offset is zero. Operating temperature is from -40 degC to 85 degC Ra = 1.8kΩ, Rb = 700Ω, Rc = 300Ω all are 5% resistor tolerance Maximum switch resistance is 50Ω Must be protected from shorts to ground and battery Must survive reverse battery Must survive failed alternator and double battery for one minute Minimum wetting current is 1mA Charlie Richlie Page 1 of 8 Micro analog input example.xmcd 12/1/2005
    Analysis plan Show A/D input can distinguish between the following switch states with no overlap. All switches open Switch A closed, B and C open Switch A and B closed, switch C open Switch A, B and C closed Show A/D input at micro will not exceed 5V Show minimum wetting current is not less than 1mA Calculate circuit response time Calculate power and temperature of R1 Show the 5V supply will not sore during a short Variables k := 1000 m 1 10 3− := ⋅ M 1 106 := ⋅ μ := 1 10 6− ⋅ OK := "OK" Fail := "Does not meet requirements" n := degC 1:= 1 10 9− ⋅ Declare variables to improve readability Supplies Vbat := 13.5V Vcc := 5V Environment := 9V Vbatmin Vccmin Vcc 1 := ⋅ 2%−( Vbatmax ) := 16V Vccmax Vcc 1 := ⋅ 2%+( ) Tamb := 25degC Tambmin := 40− degC Tambmax := 105degC 50Ω 50Ω 50Ω := := := Switch parameters Rseries_amax Rseries_bmax Rseries_cmax 1.8 k⋅ Ω⋅ Ra 0.7 k⋅ Ω⋅ Rb Rc 0.3 k⋅ Ω⋅ := := := := := := 1mΩ 1mΩ 1mΩ Rseries_amin Rseries_bmin Rseries_cmin Ra 1 Rb 1 Rc 1 := := := ⋅ ⋅ Ramin Rbmin Rcmin ) 5%−( 5%−( ) ⋅ 5%−( ) Ramax Rbmax Rcmax := := := ⋅ Ra 1 Rb 1 Rc 1 ) 5%+( 5%+( ) ⋅ 5%+( ) ⋅ Resistors R1 := 750Ω R2 := 30 k⋅ Ω⋅ R1min R2min := := Rthja_0805 := 170 degC W R1 1 8%−( ⋅ R1 1 8%−( ⋅ ) ) R1max R2max := := R1 1 8%+( ⋅ R1 1 8%+( ⋅ ) ) Charlie Richlie Page 2 of 8 Micro analog input example.xmcd 12/1/2005
    Capacitors C1 := 10 n⋅ F⋅ C2 := 10 n⋅ F⋅ C1min C2min := := Micro parameters C1 1 27%−( ⋅ C2 1 27%−( ⋅ ) ) C1max C2max := := C1 1 27%+( ⋅ C1 1 27%+( ⋅ ) ) Vmicrohigh_required Ileaknom 0A ADerror 4:= := := ⋅ Vccmax 0.65 Ileakmax := Vmicrolow_required Ileakmin := 1μ A⋅ := ⋅ Vccmin 0.35 1− μ A⋅ Micro A/D conversion error is +/- 4 counts Diode Vf Analysis := 0.7V Vfmin := 0.45V Vfmax := 1.0V Find minimum and maximum value at the micro pin with all switches open. Initial guess: VN1 := 5V Given Vcc VN1 − R1 = VN1 Ra Rb+ Rc+ + Ileak VN1 Vcc R1, ( Rc, , Ileak ) := Find VN1 ) ( Ra, Rb, ( VN1min VN1 Vccmin R1max := , , Ramin , Rbmin V_all_opennom VN1 Vcc R1, := ( Ra, Rb, Rc, , , Rcmin ) Ileaknom , ) Ileakmax VN1min = 3.756 V V_all_opennom 3.944 V = VN1max VN1 Vccmax R1min := , ( , Ramax , Rbmax , Rcmax , ) Ileakmin VN1max = 4.131 V V1micro_min := V1micro_max := VN1min R2max Ileakmax − ⋅ VN1max R2max Ileakmin − ⋅ V1micro_min = 3.755 V V1micro_max = 4.132 V Charlie Richlie Page 3 of 8 Micro analog input example.xmcd 12/1/2005
    Find minimum and maximum value at the micro with Switch A closed and Switches B and C open Initial guess: VN1 := 5V Given Vcc VN1 − R1 = VN1 Rseries Rb+ Rc+ + Ileak VN1 Vcc R1, ( , Rb, Rc, , Ileak ) := Find VN1 ) ( Rseries ( := VN1min VN1 Vccmin R1max ( V_switchA_closednom VN1 Vcc R1, := , , Rseries_amin , Rbmin , Rcmin , Rseries_amin Rb, Rc, , , ) Ileakmax ) Ileaknom VN1min = 2.644 V V_switchA_closednom 2.857 V = VN1max VN1 Vccmax R1min := , ( , Rseries_amax , Rbmax , Rcmax , ) Ileakmin VN1max = 3.135 V V2micro_min := V2micro_max := VN1min R2max Ileakmax − ⋅ VN1max R2max Ileakmin − ⋅ V2micro_min = 2.644 V V2micro_max = 3.135 V Find minimum and maximum value at the micro with Switch A and B closed and Switch C open Initial guess: VN1 := 5V Given Vcc VN1 − R1 = VN1 + Rseries_a Rseries_b + Ileak Rc+ VN1 Vcc R1, ( , , Rseries_b Rc, , Ileak ) := Find VN1 ) ( Rseries_a ( ( VN1min VN1 Vccmin R1max := , , Rseries_amin , Rseries_bmin , Rcmin , ) Ileakmax VN1min = 1.275 V VN1max VN1 Vccmax R1min := , , Rseries_amax , Rseries_bmax , Rcmax , ) Ileakmin VN1max = 1.916 V V3micro_min := V3micro_max := VN1min R2max Ileakmax − ⋅ VN1max R2max Ileakmin − ⋅ V3micro_min = 1.274 V V3micro_max = 1.916 V Charlie Richlie Page 4 of 8 Micro analog input example.xmcd 12/1/2005
    Find minimum and maximum value at the micro with Switch A, B and C closed Initial guess: VN1 := 5V Given Vcc VN1 − R1 = VN1 Rseries_a Rseries_b + + Rseries_c + Ileak VN1 Vcc R1, ( , Rseries_a , Rseries_b , Rseries_c , Ileak ) := Find VN1 ) ( VN1min VN1 Vccmin R1max := , , Rseries_amin , Rseries_bmin , Rseries_cmin , ) Ileakmax VN1min = 18.145 μ V⋅ VN1max VN1 Vccmax R1min := , , Rseries_amax , Rseries_bmax , Rseries_cmax , ) Ileakmin VN1max = 0.911 V ( ( V4micro_min := V4micro_max := VN1min R2max Ileakmax − ⋅ VN1max R2max Ileakmin − ⋅ V4micro_min = 0.792 − m V⋅ V4micro_max = 0.912 V V1micro_max = 4.132 V counts1max V1micro_max ⋅ := V1micro_min = 3.755 V counts1min V1micro_min ⋅ := V2micro_max = 3.135 V counts2max V2micro_max ⋅ := V2micro_min = 2.644 V counts2min V2micro_min ⋅ := V3micro_max = 1.916 V counts3max V3micro_max ⋅ := 1023 Vccmin 1023 Vccmax 1023 Vccmin 1023 Vccmax 1023 Vccmin 1023 Vccmax 1023 Vccmin 1023 Vccmax V3micro_min = 1.274 V counts3min V3micro_min ⋅ := V4micro_max = 0.912 V counts4max V4micro_max ⋅ := V4micro_min = 7.919 − × 10 4− V counts4min V4micro_min ⋅ := Charlie Richlie Page 5 of 8 Micro analog input example.xmcd 12/1/2005
    counts1max counts1min counts2max counts2min counts3max counts3min counts4max counts4min = 862.649 = 753.162 = 654.576 = 530.283 = 400.109 = 255.615 = 190.33 −= 0.159 if ( ⎡⎣ if ( ⎡⎣ if ( ⎡⎣ ADerror 4= Micro A/D conversion error ) counts1min ADerror − > ( ) counts2max ADerror + OK, , Fail ⎤⎦ = "OK" ) counts2min ADerror − > ( ) counts3max ADerror + OK, , Fail ⎤⎦ = "OK" ) counts3min ADerror − > ( ) counts4max ADerror + OK, , Fail ⎤⎦ = "OK" counts_decision_12 := round counts_decision_23 := round counts_decision_34 := round counts1min counts2min counts3min + 2 + 2 + 2 ⎛ ⎜ ⎝ ⎛ ⎜ ⎝ ⎛ ⎜ ⎝ counts2max counts3max counts4max ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ ⎞ ⎟ ⎠ counts_decision_12 = 704 counts_decision_23 = 465 counts_decision_34 = 223 Note: Micro A/D conversion error must also be included to ensure the different switch states can be distinguished Show A/D input at micro will not exceed Vcc ( if V1micro_max Vccmin ≤ OK, , ) Fail = "OK" Show minimum wetting current is not less than 1mA Iwetting_min := Vccmin R1max Ra+ Rb+ Rc+ Iwetting_min = 1.357 m A⋅ Charlie Richlie Page 6 of 8 Micro analog input example.xmcd 12/1/2005
    Calculate circuit response time We will find the circuit response time going from all switches open to Switch A closed. VN0 := V_all_opennom VN0 = 3.944 V V_final := V_switchA_closednom V_final = 2.857 V τ1 := R1 Rb Rc+ ) Rb Rc+ R1 ) ( ⋅ + ( C1⋅ τ1 = 4.286 μ s⋅ τ2 := R2 C2⋅ τ2 = 300 μ s⋅ Note: Because τ2 is much greater than τ1, it will dominate the slew time so we can ignore τ1. Vmicro t( ) := ( VN0 V_final − ) e ⋅ t− τ2 + V_final We will assume the response time is 5 τ2⋅ = 1.5 m s⋅ Vmicro 5 τ2⋅( ) = 2.864 V Percent_final_voltage := Percent_final_voltage = Vmicro 5 τ2⋅( ) V_final − V_final −⎛⎜ 1 ⎝ 99.744 ⋅ 100 ⎞⎟ ⎠ Calculate power and temperature of R1 Imax = 7.391 m A⋅ Imax := Vccmax R1min PR1_max := Imax 2 R1min ⋅ PR1_max = 37.696 m W⋅ TjR1_max := Tambmax + PR1_max Rthja_0805 ⋅ = TjR1_max ( if TjR1_max 111.408 degC ≤ 135degC OK, , ) Fail = "OK" Charlie Richlie Page 7 of 8 Micro analog input example.xmcd 12/1/2005
    What about the power dissipation during a short to battery? Imax = 16.087 m A⋅ Imax := Vbatmax Vccmin − R1min PR1_max := Imax 2 R1min ⋅ PR1_max = 178.565 m W⋅ TjR1_max := = TjR1_max ( if TjR1_max 55degC PR1_max Rthja_0805 + ⋅ 85.356 degC ≤ 135degC OK, , ) Fail = "OK" Show the 5V supply will not sore during a short Imax = 16.087 m A⋅ Must ensure at least a 16.1mA draw on the 5V regulator anytime a short to battery can occur on this input. One option is to add a 6.2V zener on the 5V line. Charlie Richlie Page 8 of 8 Micro analog input example.xmcd 12/1/2005
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