测量参数
\[\Phi=\Phi_{D C}+\Delta \Phi \cos \left(\omega_{p} t\right)\]这部分把参放当成比特想，接入两个线，一个用直流源接bias，一个微波源接pump。
比较简单的一种是用的二倍频。
pump参数
- pump bias （bias） z线
- pump frequency (fc) 微波源频率
- pump power （uwavePower）微波源功率
（signal power/frequency等不用参放也能确定）
pump测量
根据所需读取的signal frequency 选择合适的pump bias。然后如果是二倍频原理的参放，那么pump frequency选择读取频率的二倍，加几MHz的差值（这里和比特f10与微波源混的fc一样，基带频率和混频频率过于接近会使混出来的信号很差），例如$f_{sig} = 6.6~\mathrm{GHz}, f_{pump} = 13.203 ~\mathrm{GHz}$。
pump bias 与pump power的二维图，提取增益大，噪声小的点作为参放工作点。
工作点
- 选取原则简单来说就是：增益大，噪声小
噪声温度
具体理论参考文献，以下为代码内容，大致方法是差不多的。
在不同参数下，开与不开参放，测得$A_1,A_0$，每个点会重复测量，因此一般储存下对应的均值$E$和标准差$D$
\[\mathrm{Gain} = E(A_1)/E(A_0)\]用dB为单位则是
\[\mathrm{Gain} = E(A_1) -E(A_0), ~~\mathrm{(dB)}\]然后开与不开的信号对应的方差（记录下的是标准差，所以用平方）
\[\alpha = \left(\frac{D(A_1)}{D(A_0)}\right)^2\]最后计算，（本来有一些常数系数，但可以忽略）
\[T_{noise} = (\alpha - 1) \frac{2}{\mathrm{Gain}}\]1
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def paramp_noise_tem(dv, dataset=5, dataset_floor=20, session =['','xx','xxx'],
gain_cut=15, t_cut=0.5, des=''):
"""
Calculate the noise temperature of paramp Tp.
We assume that the noise temperature of HEMT Th is 2 K. In fact, the noise temperature we get is the sum of noise temperature of paramp and signal.
dataset: The dataset when pump on
datasetFloor: The dataset when pump off
"""
data = ds.getDataset(dv, dataset, session)
data_floor = ds.getDataset(dv, dataset_floor, session)
mat, info = ds.columns2Matrix(data, dependentColumn=[2,3,4,5,6])
mat_floor, info_floor = ds.columns2Matrix(data_floor, dependentColumn=[2,3,4,5,6])
xs = np.arange(info['Xmin'], info['Xmax']+info['Xstep']/10., info['Xstep'])
ys = np.arange(info['Ymin'], info['Ymax']+info['Ystep']/10., info['Ystep'])
gain_db = mat[:,:,1] - np.average(mat_floor[:, :, 1], 0)
alpha = (mat[:,:,2]/np.average(mat_floor[:,:,2], 0))**2
gain = 10**((gain_db-3)/10)
noise_tem = 2 / (gain) * (alpha - 1)
for idx0 in xrange(noise_tem.shape[0]):
for idx1 in xrange(noise_tem.shape[1]):
if noise_tem[idx0, idx1] >= 1:
noise_tem[idx0, idx1] = 1
if noise_tem[idx0, idx1] <= 0:
noise_tem[idx0, idx1] = 0
optimal_points = []
for idx0 in xrange(gain_db.shape[0]):
for idx1 in xrange(gain_db.shape[1]):
if gain_db[idx0, idx1] >= gain_cut and noise_tem[idx0, idx1] <= t_cut:
optimal_points.append([xs[idx0], ys[idx1]])
noise_tem
print 'maximal gain %.3f dB'%np.max( gain_db)
optimal_points = np.array(optimal_points)
# print 'gain for maximal SNR: %.3f dB'%gain_db[optimal_points[idx_max][0], optimal_points[idx_max][1]]
# print 'deviation for maximal SNR: %.3f'%mat_dev[optimal_points[idx_max][0], optimal_points[idx_max][1]]
# print 'pump power for maximal SNR: %.3f dBm'%xs[optimal_points[idx_max][0]]
# print 'pump bias for maximal SNR: %.3f V'%ys[optimal_points[idx_max][1]]
# print 'Tp for maximal SNR: %.3f K'%Tp[optimal_points[idx_max][0], optimal_points[idx_max][1]]
# print 'N1 for maximal SNR: %.3f'%data_floor_dev[optimal_points[idx_max][1]]
extent = [info['Ymin'], info['Ymax'], info['Xmin'], info['Xmax']]
figure()
imshow(gain_db, extent=extent, origin='lower', aspect='auto', interpolation='nearest',vmin = 14)
# plot(ys[optimal_points[idx_max][1]],xs[optimal_points[idx_max][0]],'o',markersize = 10,markerfacecolor = "w",markeredgecolor = "k")
plot(optimal_points[:,1], optimal_points[:,0], 'o',markersize = 15,markerfacecolor = "w",markeredgecolor = "k" )
ylabel('Pump Power (dBm)', size=18)
xlabel('Flux Bias (V)', size=18)
xticks(size=18)
yticks(size=18)
plt.ylim(info['Xmin'], info['Xmax'])
plt.xlim(info['Ymin'], info['Ymax'])
title('Gain' + des,size = 18)
colorbar().set_label("dB",size = 18)
figure()
imshow(noise_tem, extent=extent, origin='lower', aspect='auto', interpolation='nearest')
plot(optimal_points[:,1], optimal_points[:,0], 'o',markersize = 15,markerfacecolor = "w",markeredgecolor = "k" )
# plot(ys[optimal_points[idx_max][1]],xs[optimal_points[idx_max][0]],'o',markersize = 10,markerfacecolor = "w",markeredgecolor = "k")
ylabel('Pump Power (dBm)', size=18)
xlabel('Flux Bias (V)', size=18)
xticks(size=18)
yticks(size=18)
title('Noise Temperature'+ des,size = 18)
colorbar().set_label("K",size = 18)
plt.ylim(info['Xmin'], info['Xmax'])
plt.xlim(info['Ymin'], info['Ymax'])